{"id":72681,"date":"2025-05-04T02:10:19","date_gmt":"2025-05-04T02:10:19","guid":{"rendered":"https:\/\/www.europesays.com\/uk\/72681\/"},"modified":"2025-05-04T02:10:19","modified_gmt":"2025-05-04T02:10:19","slug":"strongly-interacting-meissner-phases-in-large-bosonic-flux-ladders","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/uk\/72681\/","title":{"rendered":"Strongly interacting Meissner phases in large bosonic flux ladders"},"content":{"rendered":"<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"1.\">\n<p class=\"c-article-references__text\" id=\"ref-CR1\">Eckardt, A. Colloquium: atomic quantum gases in periodically driven optical lattices. Rev. Mod. Phys. <b>89<\/b>, 011004 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.89.011004\" data-track-item_id=\"10.1103\/RevModPhys.89.011004\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.89.011004\" aria-label=\"Article reference 1\" data-doi=\"10.1103\/RevModPhys.89.011004\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017RvMP...89a1004E\" aria-label=\"ADS reference 1\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3637218\" aria-label=\"MathSciNet reference 1\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 1\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Colloquium%3A%20atomic%20quantum%20gases%20in%20periodically%20driven%20optical%20lattices&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.89.011004&amp;volume=89&amp;publication_year=2017&amp;author=Eckardt%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"2.\">\n<p class=\"c-article-references__text\" id=\"ref-CR2\">Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. <b>91<\/b>, 015006 (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.91.015006\" data-track-item_id=\"10.1103\/RevModPhys.91.015006\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.91.015006\" aria-label=\"Article reference 2\" data-doi=\"10.1103\/RevModPhys.91.015006\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019RvMP...91a5006O\" aria-label=\"ADS reference 2\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3942981\" aria-label=\"MathSciNet reference 2\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 2\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20photonics&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.91.015006&amp;volume=91&amp;publication_year=2019&amp;author=Ozawa%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"3.\">\n<p class=\"c-article-references__text\" id=\"ref-CR3\">Goldman, N. &amp; Dalibard, J. Periodically driven quantum systems: effective Hamiltonians and engineered gauge fields. Phys. Rev. X <b>4<\/b>, 031027 (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 3\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Periodically%20driven%20quantum%20systems%3A%20effective%20Hamiltonians%20and%20engineered%20gauge%20fields&amp;journal=Phys.%20Rev.%20X&amp;volume=4&amp;publication_year=2014&amp;author=Goldman%2CN&amp;author=Dalibard%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"4.\">\n<p class=\"c-article-references__text\" id=\"ref-CR4\">Bukov, M., D\u2019Alessio, L. &amp; Polkovnikov, A. Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering. Adv. Phys. <b>64<\/b>, 139 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1080\/00018732.2015.1055918\" data-track-item_id=\"10.1080\/00018732.2015.1055918\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1080%2F00018732.2015.1055918\" aria-label=\"Article reference 4\" data-doi=\"10.1080\/00018732.2015.1055918\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015AdPhy..64..139B\" aria-label=\"ADS reference 4\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 4\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Universal%20high-frequency%20behavior%20of%20periodically%20driven%20systems%3A%20from%20dynamical%20stabilization%20to%20Floquet%20engineering&amp;journal=Adv.%20Phys.&amp;doi=10.1080%2F00018732.2015.1055918&amp;volume=64&amp;publication_year=2015&amp;author=Bukov%2CM&amp;author=D%E2%80%99Alessio%2CL&amp;author=Polkovnikov%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"5.\">\n<p class=\"c-article-references__text\" id=\"ref-CR5\">Roushan, P. et al. Chiral ground-state currents of interacting photons in a synthetic magnetic field. Nat. Phys. <b>13<\/b>, 146 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys3930\" data-track-item_id=\"10.1038\/nphys3930\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys3930\" aria-label=\"Article reference 5\" data-doi=\"10.1038\/nphys3930\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 5\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20ground-state%20currents%20of%20interacting%20photons%20in%20a%20synthetic%20magnetic%20field&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys3930&amp;volume=13&amp;publication_year=2017&amp;author=Roushan%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"6.\">\n<p class=\"c-article-references__text\" id=\"ref-CR6\">Rosen, I. T. et al. A synthetic magnetic vector potential in a 2D superconducting qubit array. Nat. Phys. <b>20<\/b>, 1881\u20131887 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-024-02661-3\" data-track-item_id=\"10.1038\/s41567-024-02661-3\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-024-02661-3\" aria-label=\"Article reference 6\" data-doi=\"10.1038\/s41567-024-02661-3\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 6\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20synthetic%20magnetic%20vector%20potential%20in%20a%202D%20superconducting%20qubit%20array&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-024-02661-3&amp;volume=20&amp;pages=1881-1887&amp;publication_year=2024&amp;author=Rosen%2CIT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"7.\">\n<p class=\"c-article-references__text\" id=\"ref-CR7\">Scholl, P. et al. Microwave engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms. PRX Quantum <b>3<\/b>, 020303 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PRXQuantum.3.020303\" data-track-item_id=\"10.1103\/PRXQuantum.3.020303\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPRXQuantum.3.020303\" aria-label=\"Article reference 7\" data-doi=\"10.1103\/PRXQuantum.3.020303\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022PRXQ....3b0303S\" aria-label=\"ADS reference 7\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 7\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Microwave%20engineering%20of%20programmable%20XXZ%20Hamiltonians%20in%20arrays%20of%20Rydberg%20atoms&amp;journal=PRX%20Quantum&amp;doi=10.1103%2FPRXQuantum.3.020303&amp;volume=3&amp;publication_year=2022&amp;author=Scholl%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"8.\">\n<p class=\"c-article-references__text\" id=\"ref-CR8\">Zhao, L., Lee, M. D. K., Aliyu, M. M. &amp; Loh, H. Floquet-tailored Rydberg interactions. Nat. Commun. <b>14<\/b>, 7128 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-023-42899-8\" data-track-item_id=\"10.1038\/s41467-023-42899-8\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-023-42899-8\" aria-label=\"Article reference 8\" data-doi=\"10.1038\/s41467-023-42899-8\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023NatCo..14.7128Z\" aria-label=\"ADS reference 8\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 8\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Floquet-tailored%20Rydberg%20interactions&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-023-42899-8&amp;volume=14&amp;publication_year=2023&amp;author=Zhao%2CL&amp;author=Lee%2CMDK&amp;author=Aliyu%2CMM&amp;author=Loh%2CH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"9.\">\n<p class=\"c-article-references__text\" id=\"ref-CR9\">McIver, J. W. et al. Light-induced anomalous Hall effect in graphene. Nat. Phys. <b>16<\/b>, 38 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-019-0698-y\" data-track-item_id=\"10.1038\/s41567-019-0698-y\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-019-0698-y\" aria-label=\"Article reference 9\" data-doi=\"10.1038\/s41567-019-0698-y\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 9\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Light-induced%20anomalous%20Hall%20effect%20in%20graphene&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-019-0698-y&amp;volume=16&amp;publication_year=2020&amp;author=McIver%2CJW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"10.\">\n<p class=\"c-article-references__text\" id=\"ref-CR10\">Weitz, T. et al. Lightwave-driven electrons in a Floquet topological insulator. Preprint at <a href=\"http:\/\/arxiv.org\/abs\/2407.17917\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"http:\/\/arxiv.org\/abs\/2407.17917\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/2407.17917<\/a> (2024).<\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"11.\">\n<p class=\"c-article-references__text\" id=\"ref-CR11\">Aidelsburger, M., Nascimb\u00e9ne, S. &amp; Goldman, N. Artificial gauge fields in materials and engineered systems. C. R. Phys. <b>19<\/b>, 394 (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.crhy.2018.03.002\" data-track-item_id=\"10.1016\/j.crhy.2018.03.002\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.crhy.2018.03.002\" aria-label=\"Article reference 11\" data-doi=\"10.1016\/j.crhy.2018.03.002\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018CRPhy..19..394A\" aria-label=\"ADS reference 11\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 11\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Artificial%20gauge%20fields%20in%20materials%20and%20engineered%20systems&amp;journal=C.%20R.%20Phys.&amp;doi=10.1016%2Fj.crhy.2018.03.002&amp;volume=19&amp;publication_year=2018&amp;author=Aidelsburger%2CM&amp;author=Nascimb%C3%A9ne%2CS&amp;author=Goldman%2CN\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"12.\">\n<p class=\"c-article-references__text\" id=\"ref-CR12\">Cooper, N. R., Dalibard, J. &amp; Spielman, I. B. Topological bands for ultracold atoms. Rev. Mod. Phys. <b>91<\/b>, 015005 (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.91.015005\" data-track-item_id=\"10.1103\/RevModPhys.91.015005\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.91.015005\" aria-label=\"Article reference 12\" data-doi=\"10.1103\/RevModPhys.91.015005\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019RvMP...91a5005C\" aria-label=\"ADS reference 12\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3942980\" aria-label=\"MathSciNet reference 12\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 12\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20bands%20for%20ultracold%20atoms&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.91.015005&amp;volume=91&amp;publication_year=2019&amp;author=Cooper%2CNR&amp;author=Dalibard%2CJ&amp;author=Spielman%2CIB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"13.\">\n<p class=\"c-article-references__text\" id=\"ref-CR13\">Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. <b>303<\/b>, 2 (2003).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/S0003-4916(02)00018-0\" data-track-item_id=\"10.1016\/S0003-4916(02)00018-0\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2FS0003-4916%2802%2900018-0\" aria-label=\"Article reference 13\" data-doi=\"10.1016\/S0003-4916(02)00018-0\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2003AnPhy.303....2K\" aria-label=\"ADS reference 13\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1951039\" aria-label=\"MathSciNet reference 13\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 13\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Fault-tolerant%20quantum%20computation%20by%20anyons&amp;journal=Ann.%20Phys.&amp;doi=10.1016%2FS0003-4916%2802%2900018-0&amp;volume=303&amp;publication_year=2003&amp;author=Kitaev%2CAY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"14.\">\n<p class=\"c-article-references__text\" id=\"ref-CR14\">Nayak, C., Simon, S. H., Stern, A., Freedman, M. &amp; Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. <b>80<\/b>, 1083 (2008).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.80.1083\" data-track-item_id=\"10.1103\/RevModPhys.80.1083\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.80.1083\" aria-label=\"Article reference 14\" data-doi=\"10.1103\/RevModPhys.80.1083\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2008RvMP...80.1083N\" aria-label=\"ADS reference 14\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=2443722\" aria-label=\"MathSciNet reference 14\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 14\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Non-Abelian%20anyons%20and%20topological%20quantum%20computation&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.80.1083&amp;volume=80&amp;publication_year=2008&amp;author=Nayak%2CC&amp;author=Simon%2CSH&amp;author=Stern%2CA&amp;author=Freedman%2CM&amp;author=Sarma%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"15.\">\n<p class=\"c-article-references__text\" id=\"ref-CR15\">D\u2019Alessio, L. &amp; Rigol, M. Long-time behavior of isolated periodically driven interacting lattice systems. Phys. Rev. X <b>4<\/b>, 041048 (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 15\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Long-time%20behavior%20of%20isolated%20periodically%20driven%20interacting%20lattice%20systems&amp;journal=Phys.%20Rev.%20X&amp;volume=4&amp;publication_year=2014&amp;author=D%E2%80%99Alessio%2CL&amp;author=Rigol%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"16.\">\n<p class=\"c-article-references__text\" id=\"ref-CR16\">Lazarides, A., Das, A. &amp; Moessner, R. Equilibrium states of generic quantum systems subject to periodic driving. Phys. Rev. E <b>90<\/b>, 012110 (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevE.90.012110\" data-track-item_id=\"10.1103\/PhysRevE.90.012110\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevE.90.012110\" aria-label=\"Article reference 16\" data-doi=\"10.1103\/PhysRevE.90.012110\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvE..90a2110L\" aria-label=\"ADS reference 16\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 16\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Equilibrium%20states%20of%20generic%20quantum%20systems%20subject%20to%20periodic%20driving&amp;journal=Phys.%20Rev.%20E&amp;doi=10.1103%2FPhysRevE.90.012110&amp;volume=90&amp;publication_year=2014&amp;author=Lazarides%2CA&amp;author=Das%2CA&amp;author=Moessner%2CR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"17.\">\n<p class=\"c-article-references__text\" id=\"ref-CR17\">Ponte, P., Chandran, A., Papi\u0107, Z. &amp; Abanin, D. A. Periodically driven ergodic and many-body localized quantum systems. Ann. Phys. <b>353<\/b>, 196 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.aop.2014.11.008\" data-track-item_id=\"10.1016\/j.aop.2014.11.008\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.aop.2014.11.008\" aria-label=\"Article reference 17\" data-doi=\"10.1016\/j.aop.2014.11.008\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015AnPhy.353..196P\" aria-label=\"ADS reference 17\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3322961\" aria-label=\"MathSciNet reference 17\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 17\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Periodically%20driven%20ergodic%20and%20many-body%20localized%20quantum%20systems&amp;journal=Ann.%20Phys.&amp;doi=10.1016%2Fj.aop.2014.11.008&amp;volume=353&amp;publication_year=2015&amp;author=Ponte%2CP&amp;author=Chandran%2CA&amp;author=Papi%C4%87%2CZ&amp;author=Abanin%2CDA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"18.\">\n<p class=\"c-article-references__text\" id=\"ref-CR18\">Thanasilp, S., Tangpanitanon, J., Lemonde, M.-A., Dangniam, N. &amp; Angelakis, D. G. Quantum supremacy and quantum phase transitions. Phys. Rev. B <b>103<\/b>, 165132 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.103.165132\" data-track-item_id=\"10.1103\/PhysRevB.103.165132\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.103.165132\" aria-label=\"Article reference 18\" data-doi=\"10.1103\/PhysRevB.103.165132\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhRvB.103p5132T\" aria-label=\"ADS reference 18\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 18\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20supremacy%20and%20quantum%20phase%20transitions&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.103.165132&amp;volume=103&amp;publication_year=2021&amp;author=Thanasilp%2CS&amp;author=Tangpanitanon%2CJ&amp;author=Lemonde%2CM-A&amp;author=Dangniam%2CN&amp;author=Angelakis%2CDG\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"19.\">\n<p class=\"c-article-references__text\" id=\"ref-CR19\">Zheng, Y.-G. et al. Efficiently extracting multi-point correlations of a Floquet thermalized system. Preprint at <a href=\"http:\/\/arxiv.org\/abs\/2210.08556\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"http:\/\/arxiv.org\/abs\/2210.08556\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/2210.08556<\/a> (2022).<\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"20.\">\n<p class=\"c-article-references__text\" id=\"ref-CR20\">Bilitewski, T. &amp; Cooper, N. R. Population dynamics in a Floquet realization of the Harper-Hofstadter Hamiltonian. Phys. Rev. A <b>91<\/b>, 063611 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.91.063611\" data-track-item_id=\"10.1103\/PhysRevA.91.063611\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.91.063611\" aria-label=\"Article reference 20\" data-doi=\"10.1103\/PhysRevA.91.063611\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015PhRvA..91f3611B\" aria-label=\"ADS reference 20\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 20\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Population%20dynamics%20in%20a%20Floquet%20realization%20of%20the%20Harper-Hofstadter%20Hamiltonian&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.91.063611&amp;volume=91&amp;publication_year=2015&amp;author=Bilitewski%2CT&amp;author=Cooper%2CNR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"21.\">\n<p class=\"c-article-references__text\" id=\"ref-CR21\">Bilitewski, T. &amp; Cooper, N. R. Scattering theory for Floquet-Bloch states. Phys. Rev. A <b>91<\/b>, 033601 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.91.033601\" data-track-item_id=\"10.1103\/PhysRevA.91.033601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.91.033601\" aria-label=\"Article reference 21\" data-doi=\"10.1103\/PhysRevA.91.033601\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015PhRvA..91c3601B\" aria-label=\"ADS reference 21\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3413998\" aria-label=\"MathSciNet reference 21\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 21\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Scattering%20theory%20for%20Floquet-Bloch%20states&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.91.033601&amp;volume=91&amp;publication_year=2015&amp;author=Bilitewski%2CT&amp;author=Cooper%2CNR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"22.\">\n<p class=\"c-article-references__text\" id=\"ref-CR22\">Tai, M. E. et al. Microscopy of the interacting Harper-Hofstadter model in the few-body limit. Nature <b>546<\/b>, 519 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature22811\" data-track-item_id=\"10.1038\/nature22811\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature22811\" aria-label=\"Article reference 22\" data-doi=\"10.1038\/nature22811\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017Natur.546..519T\" aria-label=\"ADS reference 22\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 22\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Microscopy%20of%20the%20interacting%20Harper-Hofstadter%20model%20in%20the%20few-body%20limit&amp;journal=Nature&amp;doi=10.1038%2Fnature22811&amp;volume=546&amp;publication_year=2017&amp;author=Tai%2CME\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"23.\">\n<p class=\"c-article-references__text\" id=\"ref-CR23\">Clark, L. W., Schine, N., Baum, C., Jia, N. &amp; Simon, J. Observation of Laughlin states made of light. Nature <b>582<\/b>, 41 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-020-2318-5\" data-track-item_id=\"10.1038\/s41586-020-2318-5\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-020-2318-5\" aria-label=\"Article reference 23\" data-doi=\"10.1038\/s41586-020-2318-5\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020Natur.582...41C\" aria-label=\"ADS reference 23\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 23\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20Laughlin%20states%20made%20of%20light&amp;journal=Nature&amp;doi=10.1038%2Fs41586-020-2318-5&amp;volume=582&amp;publication_year=2020&amp;author=Clark%2CLW&amp;author=Schine%2CN&amp;author=Baum%2CC&amp;author=Jia%2CN&amp;author=Simon%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"24.\">\n<p class=\"c-article-references__text\" id=\"ref-CR24\">L\u00e9onard, J. et al. Realization of a fractional quantum Hall state with ultracold atoms. Nature <b>619<\/b>, 495 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-023-06122-4\" data-track-item_id=\"10.1038\/s41586-023-06122-4\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-023-06122-4\" aria-label=\"Article reference 24\" data-doi=\"10.1038\/s41586-023-06122-4\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023Natur.619..495L\" aria-label=\"ADS reference 24\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 24\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Realization%20of%20a%20fractional%20quantum%20Hall%20state%20with%20ultracold%20atoms&amp;journal=Nature&amp;doi=10.1038%2Fs41586-023-06122-4&amp;volume=619&amp;publication_year=2023&amp;author=L%C3%A9onard%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"25.\">\n<p class=\"c-article-references__text\" id=\"ref-CR25\">Wang, C. et al. Realization of fractional quantum Hall state with interacting photons. Science <b>384<\/b>, 579 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.ado3912\" data-track-item_id=\"10.1126\/science.ado3912\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.ado3912\" aria-label=\"Article reference 25\" data-doi=\"10.1126\/science.ado3912\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024Sci...384..579W\" aria-label=\"ADS reference 25\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4785823\" aria-label=\"MathSciNet reference 25\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 25\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Realization%20of%20fractional%20quantum%20Hall%20state%20with%20interacting%20photons&amp;journal=Science&amp;doi=10.1126%2Fscience.ado3912&amp;volume=384&amp;publication_year=2024&amp;author=Wang%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"26.\">\n<p class=\"c-article-references__text\" id=\"ref-CR26\">Hafezi, M., S\u00f8rensen, A. S., Demler, E. &amp; Lukin, M. D. Fractional quantum Hall effect in optical lattices. Phys. Rev. A <b>76<\/b>, 023613 (2007).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.76.023613\" data-track-item_id=\"10.1103\/PhysRevA.76.023613\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.76.023613\" aria-label=\"Article reference 26\" data-doi=\"10.1103\/PhysRevA.76.023613\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2007PhRvA..76b3613H\" aria-label=\"ADS reference 26\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 26\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Fractional%20quantum%20Hall%20effect%20in%20optical%20lattices&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.76.023613&amp;volume=76&amp;publication_year=2007&amp;author=Hafezi%2CM&amp;author=S%C3%B8rensen%2CAS&amp;author=Demler%2CE&amp;author=Lukin%2CMD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"27.\">\n<p class=\"c-article-references__text\" id=\"ref-CR27\">Palmer, R. N., Klein, A. &amp; Jaksch, D. Optical lattice quantum Hall effect. Phys. Rev. A <b>78<\/b>, 013609 (2008).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.78.013609\" data-track-item_id=\"10.1103\/PhysRevA.78.013609\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.78.013609\" aria-label=\"Article reference 27\" data-doi=\"10.1103\/PhysRevA.78.013609\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2008PhRvA..78a3609P\" aria-label=\"ADS reference 27\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 27\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optical%20lattice%20quantum%20Hall%20effect&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.78.013609&amp;volume=78&amp;publication_year=2008&amp;author=Palmer%2CRN&amp;author=Klein%2CA&amp;author=Jaksch%2CD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"28.\">\n<p class=\"c-article-references__text\" id=\"ref-CR28\">M\u00f6ller, G. &amp; Cooper, N. R. Composite fermion theory for bosonic quantum Hall states on lattices. Phys. Rev. Lett. <b>103<\/b>, 105303 (2009).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.103.105303\" data-track-item_id=\"10.1103\/PhysRevLett.103.105303\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.103.105303\" aria-label=\"Article reference 28\" data-doi=\"10.1103\/PhysRevLett.103.105303\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2009PhRvL.103j5303M\" aria-label=\"ADS reference 28\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 28\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Composite%20fermion%20theory%20for%20bosonic%20quantum%20Hall%20states%20on%20lattices&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.103.105303&amp;volume=103&amp;publication_year=2009&amp;author=M%C3%B6ller%2CG&amp;author=Cooper%2CNR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"29.\">\n<p class=\"c-article-references__text\" id=\"ref-CR29\">Dhar, A. et al. Bose-Hubbard model in a strong effective magnetic field: emergence of a chiral Mott insulator ground state. Phys. Rev. A <b>85<\/b>, 041602 (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.85.041602\" data-track-item_id=\"10.1103\/PhysRevA.85.041602\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.85.041602\" aria-label=\"Article reference 29\" data-doi=\"10.1103\/PhysRevA.85.041602\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2012PhRvA..85d1602D\" aria-label=\"ADS reference 29\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 29\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Bose-Hubbard%20model%20in%20a%20strong%20effective%20magnetic%20field%3A%20emergence%20of%20a%20chiral%20Mott%20insulator%20ground%20state&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.85.041602&amp;volume=85&amp;publication_year=2012&amp;author=Dhar%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"30.\">\n<p class=\"c-article-references__text\" id=\"ref-CR30\">Piraud, M. et al. Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder. Phys. Rev. B <b>91<\/b>, 140406 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.91.140406\" data-track-item_id=\"10.1103\/PhysRevB.91.140406\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.91.140406\" aria-label=\"Article reference 30\" data-doi=\"10.1103\/PhysRevB.91.140406\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015PhRvB..91n0406P\" aria-label=\"ADS reference 30\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 30\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Vortex%20and%20Meissner%20phases%20of%20strongly%20interacting%20bosons%20on%20a%20two-leg%20ladder&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.91.140406&amp;volume=91&amp;publication_year=2015&amp;author=Piraud%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"31.\">\n<p class=\"c-article-references__text\" id=\"ref-CR31\">Greschner, S. et al. Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: swimming against the tide. Phys. Rev. Lett. <b>115<\/b>, 190402 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.115.190402\" data-track-item_id=\"10.1103\/PhysRevLett.115.190402\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.115.190402\" aria-label=\"Article reference 31\" data-doi=\"10.1103\/PhysRevLett.115.190402\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015PhRvL.115s0402G\" aria-label=\"ADS reference 31\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 31\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Spontaneous%20increase%20of%20magnetic%20flux%20and%20chiral-current%20reversal%20in%20bosonic%20ladders%3A%20swimming%20against%20the%20tide&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.115.190402&amp;volume=115&amp;publication_year=2015&amp;author=Greschner%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"32.\">\n<p class=\"c-article-references__text\" id=\"ref-CR32\">Greschner, S. et al. Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field. Phys. Rev. A <b>94<\/b>, 063628 (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.94.063628\" data-track-item_id=\"10.1103\/PhysRevA.94.063628\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.94.063628\" aria-label=\"Article reference 32\" data-doi=\"10.1103\/PhysRevA.94.063628\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016PhRvA..94f3628G\" aria-label=\"ADS reference 32\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 32\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Symmetry-broken%20states%20in%20a%20system%20of%20interacting%20bosons%20on%20a%20two-leg%20ladder%20with%20a%20uniform%20Abelian%20gauge%20field&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.94.063628&amp;volume=94&amp;publication_year=2016&amp;author=Greschner%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"33.\">\n<p class=\"c-article-references__text\" id=\"ref-CR33\">Di Dio, M., De Palo, S., Orignac, E., Citro, R. &amp; Chiofalo, M.-L. Persisting Meissner state and incommensurate phases of hard-core boson ladders in a flux. Phys. Rev. B <b>92<\/b>, 060506 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.92.060506\" data-track-item_id=\"10.1103\/PhysRevB.92.060506\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.92.060506\" aria-label=\"Article reference 33\" data-doi=\"10.1103\/PhysRevB.92.060506\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015PhRvB..92f0506D\" aria-label=\"ADS reference 33\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 33\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Persisting%20Meissner%20state%20and%20incommensurate%20phases%20of%20hard-core%20boson%20ladders%20in%20a%20flux&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.92.060506&amp;volume=92&amp;publication_year=2015&amp;author=Dio%2CM&amp;author=Palo%2CS&amp;author=Orignac%2CE&amp;author=Citro%2CR&amp;author=Chiofalo%2CM-L\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"34.\">\n<p class=\"c-article-references__text\" id=\"ref-CR34\">Citro, R., Giamarchi, T. &amp; Orignac, E. Hall response in interacting bosonic and fermionic ladders. Phys. Rev. Lett. <b>134<\/b>, 056501 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.134.056501\" data-track-item_id=\"10.1103\/PhysRevLett.134.056501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.134.056501\" aria-label=\"Article reference 34\" data-doi=\"10.1103\/PhysRevLett.134.056501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 34\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Hall%20response%20in%20interacting%20bosonic%20and%20fermionic%20ladders&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.134.056501&amp;volume=134&amp;publication_year=2025&amp;author=Citro%2CR&amp;author=Giamarchi%2CT&amp;author=Orignac%2CE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"35.\">\n<p class=\"c-article-references__text\" id=\"ref-CR35\">Buser, M., Greschner, S., Schollw\u00f6ck, U. &amp; Giamarchi, T. Probing the Hall voltage in synthetic quantum systems. Phys. Rev. Lett. <b>126<\/b>, 030501 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.126.030501\" data-track-item_id=\"10.1103\/PhysRevLett.126.030501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.126.030501\" aria-label=\"Article reference 35\" data-doi=\"10.1103\/PhysRevLett.126.030501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhRvL.126c0501B\" aria-label=\"ADS reference 35\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 35\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Probing%20the%20Hall%20voltage%20in%20synthetic%20quantum%20systems&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.126.030501&amp;volume=126&amp;publication_year=2021&amp;author=Buser%2CM&amp;author=Greschner%2CS&amp;author=Schollw%C3%B6ck%2CU&amp;author=Giamarchi%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"36.\">\n<p class=\"c-article-references__text\" id=\"ref-CR36\">Buser, M., Schollw\u00f6ck, U. &amp; Grusdt, F. Snapshot-based characterization of particle currents and the Hall response in synthetic flux lattices. Phys. Rev. A <b>105<\/b>, 033303 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.105.033303\" data-track-item_id=\"10.1103\/PhysRevA.105.033303\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.105.033303\" aria-label=\"Article reference 36\" data-doi=\"10.1103\/PhysRevA.105.033303\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022PhRvA.105c3303B\" aria-label=\"ADS reference 36\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 36\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Snapshot-based%20characterization%20of%20particle%20currents%20and%20the%20Hall%20response%20in%20synthetic%20flux%20lattices&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.105.033303&amp;volume=105&amp;publication_year=2022&amp;author=Buser%2CM&amp;author=Schollw%C3%B6ck%2CU&amp;author=Grusdt%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"37.\">\n<p class=\"c-article-references__text\" id=\"ref-CR37\">Atala, M. et al. Observation of chiral currents with ultracold atoms in bosonic ladders. Nat. Phys <b>10<\/b>, 588 (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys2998\" data-track-item_id=\"10.1038\/nphys2998\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys2998\" aria-label=\"Article reference 37\" data-doi=\"10.1038\/nphys2998\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 37\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20chiral%20currents%20with%20ultracold%20atoms%20in%20bosonic%20ladders&amp;journal=Nat.%20Phys&amp;doi=10.1038%2Fnphys2998&amp;volume=10&amp;publication_year=2014&amp;author=Atala%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"38.\">\n<p class=\"c-article-references__text\" id=\"ref-CR38\">Mancini, M. et al. Observation of chiral edge states with neutral fermions in synthetic Hall ribbons. Science <b>349<\/b>, 1510 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.aaa8736\" data-track-item_id=\"10.1126\/science.aaa8736\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.aaa8736\" aria-label=\"Article reference 38\" data-doi=\"10.1126\/science.aaa8736\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015Sci...349.1510M\" aria-label=\"ADS reference 38\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3444386\" aria-label=\"MathSciNet reference 38\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 38\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20chiral%20edge%20states%20with%20neutral%20fermions%20in%20synthetic%20Hall%20ribbons&amp;journal=Science&amp;doi=10.1126%2Fscience.aaa8736&amp;volume=349&amp;publication_year=2015&amp;author=Mancini%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"39.\">\n<p class=\"c-article-references__text\" id=\"ref-CR39\">Stuhl, B. K., Lu, H.-I., Aycock, L. M., Genkina, D. &amp; Spielman, I. B. Visualizing edge states with an atomic Bose gas in the quantum Hall regime. Science <b>349<\/b>, 1514 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.aaa8515\" data-track-item_id=\"10.1126\/science.aaa8515\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.aaa8515\" aria-label=\"Article reference 39\" data-doi=\"10.1126\/science.aaa8515\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015Sci...349.1514S\" aria-label=\"ADS reference 39\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3444387\" aria-label=\"MathSciNet reference 39\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 39\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Visualizing%20edge%20states%20with%20an%20atomic%20Bose%20gas%20in%20the%20quantum%20Hall%20regime&amp;journal=Science&amp;doi=10.1126%2Fscience.aaa8515&amp;volume=349&amp;publication_year=2015&amp;author=Stuhl%2CBK&amp;author=Lu%2CH-I&amp;author=Aycock%2CLM&amp;author=Genkina%2CD&amp;author=Spielman%2CIB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"40.\">\n<p class=\"c-article-references__text\" id=\"ref-CR40\">Zhou, T.-W. et al. Observation of universal Hall response in strongly interacting fermions. Science <b>381<\/b>, 427 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.add1969\" data-track-item_id=\"10.1126\/science.add1969\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.add1969\" aria-label=\"Article reference 40\" data-doi=\"10.1126\/science.add1969\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023Sci...381..427Z\" aria-label=\"ADS reference 40\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 40\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20universal%20Hall%20response%20in%20strongly%20interacting%20fermions&amp;journal=Science&amp;doi=10.1126%2Fscience.add1969&amp;volume=381&amp;publication_year=2023&amp;author=Zhou%2CT-W\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"41.\">\n<p class=\"c-article-references__text\" id=\"ref-CR41\">T.-W., Zhou et al. Measuring Hall voltage and Hall resistance in an atom-based quantum simulator. Preprint at <a href=\"http:\/\/arxiv.org\/abs\/2411.09744\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"http:\/\/arxiv.org\/abs\/2411.09744\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/2411.09744<\/a> (2024).<\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"42.\">\n<p class=\"c-article-references__text\" id=\"ref-CR42\">Liang, Q. et al. Chiral dynamics of ultracold atoms under a tunable SU(2) synthetic gauge field. Nat. Phys. <b>20<\/b>, 1738 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-024-02644-4\" data-track-item_id=\"10.1038\/s41567-024-02644-4\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-024-02644-4\" aria-label=\"Article reference 42\" data-doi=\"10.1038\/s41567-024-02644-4\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 42\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20dynamics%20of%20ultracold%20atoms%20under%20a%20tunable%20SU%282%29%20synthetic%20gauge%20field&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-024-02644-4&amp;volume=20&amp;publication_year=2024&amp;author=Liang%2CQ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"43.\">\n<p class=\"c-article-references__text\" id=\"ref-CR43\">Chen, T. et al. Interaction-driven breakdown of Aharonov\u2013Bohm caging in flat-band Rydberg lattices. Nat. Phys. <b>21<\/b>, 221 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-024-02714-7\" data-track-item_id=\"10.1038\/s41567-024-02714-7\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-024-02714-7\" aria-label=\"Article reference 43\" data-doi=\"10.1038\/s41567-024-02714-7\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 43\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Interaction-driven%20breakdown%20of%20Aharonov%E2%80%93Bohm%20caging%20in%20flat-band%20Rydberg%20lattices&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-024-02714-7&amp;volume=21&amp;publication_year=2025&amp;author=Chen%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"44.\">\n<p class=\"c-article-references__text\" id=\"ref-CR44\">Impertro, A. et al. Local readout and control of current and kinetic energy operators in optical lattices. Phys. Rev. Lett. <b>133<\/b>, 063401 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.133.063401\" data-track-item_id=\"10.1103\/PhysRevLett.133.063401\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.133.063401\" aria-label=\"Article reference 44\" data-doi=\"10.1103\/PhysRevLett.133.063401\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 44\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Local%20readout%20and%20control%20of%20current%20and%20kinetic%20energy%20operators%20in%20optical%20lattices&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.133.063401&amp;volume=133&amp;publication_year=2024&amp;author=Impertro%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"45.\">\n<p class=\"c-article-references__text\" id=\"ref-CR45\">H\u00fcgel, D. &amp; Paredes, B. Chiral ladders and the edges of quantum Hall insulators. Phys. Rev. A <b>89<\/b>, 023619 (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.89.023619\" data-track-item_id=\"10.1103\/PhysRevA.89.023619\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.89.023619\" aria-label=\"Article reference 45\" data-doi=\"10.1103\/PhysRevA.89.023619\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvA..89b3619H\" aria-label=\"ADS reference 45\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 45\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20ladders%20and%20the%20edges%20of%20quantum%20Hall%20insulators&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.89.023619&amp;volume=89&amp;publication_year=2014&amp;author=H%C3%BCgel%2CD&amp;author=Paredes%2CB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"46.\">\n<p class=\"c-article-references__text\" id=\"ref-CR46\">Impertro, A. et al. An unsupervised deep learning algorithm for single-site reconstruction in quantum gas microscopes. Commun. Phys. <b>6<\/b>, 166 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s42005-023-01287-w\" data-track-item_id=\"10.1038\/s42005-023-01287-w\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs42005-023-01287-w\" aria-label=\"Article reference 46\" data-doi=\"10.1038\/s42005-023-01287-w\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 46\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=An%20unsupervised%20deep%20learning%20algorithm%20for%20single-site%20reconstruction%20in%20quantum%20gas%20microscopes&amp;journal=Commun.%20Phys.&amp;doi=10.1038%2Fs42005-023-01287-w&amp;volume=6&amp;publication_year=2023&amp;author=Impertro%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"47.\">\n<p class=\"c-article-references__text\" id=\"ref-CR47\">Wienand, J. F. et al. Emergence of fluctuating hydrodynamics in chaotic quantum systems. Nat. Phys. <b>20<\/b>, 1732\u20131737 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-024-02611-z\" data-track-item_id=\"10.1038\/s41567-024-02611-z\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-024-02611-z\" aria-label=\"Article reference 47\" data-doi=\"10.1038\/s41567-024-02611-z\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 47\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Emergence%20of%20fluctuating%20hydrodynamics%20in%20chaotic%20quantum%20systems&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-024-02611-z&amp;volume=20&amp;pages=1732-1737&amp;publication_year=2024&amp;author=Wienand%2CJF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"48.\">\n<p class=\"c-article-references__text\" id=\"ref-CR48\">Aidelsburger, M. et al. Experimental realization of strong effective magnetic fields in an optical lattice. Phys. Rev. Lett. <b>107<\/b>, 255301 (2011).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.107.255301\" data-track-item_id=\"10.1103\/PhysRevLett.107.255301\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.107.255301\" aria-label=\"Article reference 48\" data-doi=\"10.1103\/PhysRevLett.107.255301\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2011PhRvL.107y5301A\" aria-label=\"ADS reference 48\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 48\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Experimental%20realization%20of%20strong%20effective%20magnetic%20fields%20in%20an%20optical%20lattice&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.107.255301&amp;volume=107&amp;publication_year=2011&amp;author=Aidelsburger%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"49.\">\n<p class=\"c-article-references__text\" id=\"ref-CR49\">Harper, P. G. Single band motion of conduction electrons in a uniform magnetic field. Proc. Phys. Soc. A <b>68<\/b>, 874 (1955).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/0370-1298\/68\/10\/304\" data-track-item_id=\"10.1088\/0370-1298\/68\/10\/304\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F0370-1298%2F68%2F10%2F304\" aria-label=\"Article reference 49\" data-doi=\"10.1088\/0370-1298\/68\/10\/304\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1955PPSA...68..874H\" aria-label=\"ADS reference 49\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 49\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Single%20band%20motion%20of%20conduction%20electrons%20in%20a%20uniform%20magnetic%20field&amp;journal=Proc.%20Phys.%20Soc.%20A&amp;doi=10.1088%2F0370-1298%2F68%2F10%2F304&amp;volume=68&amp;publication_year=1955&amp;author=Harper%2CPG\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"50.\">\n<p class=\"c-article-references__text\" id=\"ref-CR50\">Hofstadter, D. R. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B <b>14<\/b>, 2239 (1976).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.14.2239\" data-track-item_id=\"10.1103\/PhysRevB.14.2239\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.14.2239\" aria-label=\"Article reference 50\" data-doi=\"10.1103\/PhysRevB.14.2239\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1976PhRvB..14.2239H\" aria-label=\"ADS reference 50\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 50\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Energy%20levels%20and%20wave%20functions%20of%20Bloch%20electrons%20in%20rational%20and%20irrational%20magnetic%20fields&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.14.2239&amp;volume=14&amp;publication_year=1976&amp;author=Hofstadter%2CDR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"51.\">\n<p class=\"c-article-references__text\" id=\"ref-CR51\">Orignac, E. &amp; Giamarchi, T. Meissner effect in a bosonic ladder. Phys. Rev. B <b>64<\/b>, 144515 (2001).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.64.144515\" data-track-item_id=\"10.1103\/PhysRevB.64.144515\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.64.144515\" aria-label=\"Article reference 51\" data-doi=\"10.1103\/PhysRevB.64.144515\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2001PhRvB..64n4515O\" aria-label=\"ADS reference 51\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 51\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Meissner%20effect%20in%20a%20bosonic%20ladder&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.64.144515&amp;volume=64&amp;publication_year=2001&amp;author=Orignac%2CE&amp;author=Giamarchi%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"52.\">\n<p class=\"c-article-references__text\" id=\"ref-CR52\">Petrescu, A. &amp; Le Hur, K. Bosonic Mott insulator with Meissner currents. Phys. Rev. Lett. <b>111<\/b>, 150601 (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.111.150601\" data-track-item_id=\"10.1103\/PhysRevLett.111.150601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.111.150601\" aria-label=\"Article reference 52\" data-doi=\"10.1103\/PhysRevLett.111.150601\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2013PhRvL.111o0601P\" aria-label=\"ADS reference 52\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 52\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Bosonic%20Mott%20insulator%20with%20Meissner%20currents&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.111.150601&amp;volume=111&amp;publication_year=2013&amp;author=Petrescu%2CA&amp;author=Hur%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"53.\">\n<p class=\"c-article-references__text\" id=\"ref-CR53\">Ke\u00dfler, S. &amp; Marquardt, F. Single-site-resolved measurement of the current statistics in optical lattices. Phys. Rev. A <b>89<\/b>, 061601 (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.89.061601\" data-track-item_id=\"10.1103\/PhysRevA.89.061601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.89.061601\" aria-label=\"Article reference 53\" data-doi=\"10.1103\/PhysRevA.89.061601\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvA..89f1601K\" aria-label=\"ADS reference 53\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 53\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Single-site-resolved%20measurement%20of%20the%20current%20statistics%20in%20optical%20lattices&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.89.061601&amp;volume=89&amp;publication_year=2014&amp;author=Ke%C3%9Fler%2CS&amp;author=Marquardt%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"54.\">\n<p class=\"c-article-references__text\" id=\"ref-CR54\">Sun, G. &amp; Eckardt, A. Optimal frequency window for Floquet engineering in optical lattices. Phys. Rev. Res. <b>2<\/b>, 013241 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevResearch.2.013241\" data-track-item_id=\"10.1103\/PhysRevResearch.2.013241\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevResearch.2.013241\" aria-label=\"Article reference 54\" data-doi=\"10.1103\/PhysRevResearch.2.013241\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 54\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optimal%20frequency%20window%20for%20Floquet%20engineering%20in%20optical%20lattices&amp;journal=Phys.%20Rev.%20Res.&amp;doi=10.1103%2FPhysRevResearch.2.013241&amp;volume=2&amp;publication_year=2020&amp;author=Sun%2CG&amp;author=Eckardt%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"55.\">\n<p class=\"c-article-references__text\" id=\"ref-CR55\">Cr\u00e9pin, F., Laflorencie, N., Roux, G. &amp; Simon, P. Phase diagram of hard-core bosons on clean and disordered two-leg ladders: Mott insulator\u2013Luttinger liquid\u2013Bose glass. Phys. Rev. B <b>84<\/b>, 054517 (2011).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.84.054517\" data-track-item_id=\"10.1103\/PhysRevB.84.054517\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.84.054517\" aria-label=\"Article reference 55\" data-doi=\"10.1103\/PhysRevB.84.054517\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2011PhRvB..84e4517C\" aria-label=\"ADS reference 55\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 55\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Phase%20diagram%20of%20hard-core%20bosons%20on%20clean%20and%20disordered%20two-leg%20ladders%3A%20Mott%20insulator%E2%80%93Luttinger%20liquid%E2%80%93Bose%20glass&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.84.054517&amp;volume=84&amp;publication_year=2011&amp;author=Cr%C3%A9pin%2CF&amp;author=Laflorencie%2CN&amp;author=Roux%2CG&amp;author=Simon%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"56.\">\n<p class=\"c-article-references__text\" id=\"ref-CR56\">Qiao, X., Zhang, X.-B., Jian, Y., Zhang, A.-X. &amp; Xue, J.-K. Quench dynamics of two-leg ladders with magnetic flux. Phys. A Stat. <b>576<\/b>, 126062 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.physa.2021.126062\" data-track-item_id=\"10.1016\/j.physa.2021.126062\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.physa.2021.126062\" aria-label=\"Article reference 56\" data-doi=\"10.1016\/j.physa.2021.126062\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4253388\" aria-label=\"MathSciNet reference 56\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 56\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quench%20dynamics%20of%20two-leg%20ladders%20with%20magnetic%20flux&amp;journal=Phys.%20A%20Stat.&amp;doi=10.1016%2Fj.physa.2021.126062&amp;volume=576&amp;publication_year=2021&amp;author=Qiao%2CX&amp;author=Zhang%2CX-B&amp;author=Jian%2CY&amp;author=Zhang%2CA-X&amp;author=Xue%2CJ-K\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"57.\">\n<p class=\"c-article-references__text\" id=\"ref-CR57\">Giri, M. K., Paul, B. &amp; Mishra, T. Flux-enhanced localization and reentrant delocalization in the quench dynamics of two interacting bosons on a Bose-Hubbard ladder. Phys. Rev. A <b>109<\/b>, 043308 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.109.043308\" data-track-item_id=\"10.1103\/PhysRevA.109.043308\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.109.043308\" aria-label=\"Article reference 57\" data-doi=\"10.1103\/PhysRevA.109.043308\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024PhRvA.109d3308G\" aria-label=\"ADS reference 57\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 57\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Flux-enhanced%20localization%20and%20reentrant%20delocalization%20in%20the%20quench%20dynamics%20of%20two%20interacting%20bosons%20on%20a%20Bose-Hubbard%20ladder&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.109.043308&amp;volume=109&amp;publication_year=2024&amp;author=Giri%2CMK&amp;author=Paul%2CB&amp;author=Mishra%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"58.\">\n<p class=\"c-article-references__text\" id=\"ref-CR58\">Jian, Y. et al. Defect induced nonequilibrium quantum dynamics in an interacting Bose\u2013Hubbard flux ladder. New J. Phys. <b>25<\/b>, 043025 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/1367-2630\/accec3\" data-track-item_id=\"10.1088\/1367-2630\/accec3\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1367-2630%2Faccec3\" aria-label=\"Article reference 58\" data-doi=\"10.1088\/1367-2630\/accec3\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023NJPh...25d3025J\" aria-label=\"ADS reference 58\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4596879\" aria-label=\"MathSciNet reference 58\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 58\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Defect%20induced%20nonequilibrium%20quantum%20dynamics%20in%20an%20interacting%20Bose%E2%80%93Hubbard%20flux%20ladder&amp;journal=New%20J.%20Phys.&amp;doi=10.1088%2F1367-2630%2Faccec3&amp;volume=25&amp;publication_year=2023&amp;author=Jian%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"59.\">\n<p class=\"c-article-references__text\" id=\"ref-CR59\">Citro, R., De Palo, S., Victorin, N., Minguzzi, A. &amp; Orignac, E. Spectral function of a boson ladder in an artificial gauge field. Condens. Matter <b>5<\/b>, 15 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.3390\/condmat5010015\" data-track-item_id=\"10.3390\/condmat5010015\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.3390%2Fcondmat5010015\" aria-label=\"Article reference 59\" data-doi=\"10.3390\/condmat5010015\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 59\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Spectral%20function%20of%20a%20boson%20ladder%20in%20an%20artificial%20gauge%20field&amp;journal=Condens.%20Matter&amp;doi=10.3390%2Fcondmat5010015&amp;volume=5&amp;publication_year=2020&amp;author=Citro%2CR&amp;author=Palo%2CS&amp;author=Victorin%2CN&amp;author=Minguzzi%2CA&amp;author=Orignac%2CE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"60.\">\n<p class=\"c-article-references__text\" id=\"ref-CR60\">Huang, W. &amp; Yao, Y. Spatial inversion symmetry breaking of vortex current in a biased-ladder superfluid. Phys. Rev. Res. <b>6<\/b>, 013037 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevResearch.6.013037\" data-track-item_id=\"10.1103\/PhysRevResearch.6.013037\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevResearch.6.013037\" aria-label=\"Article reference 60\" data-doi=\"10.1103\/PhysRevResearch.6.013037\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 60\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Spatial%20inversion%20symmetry%20breaking%20of%20vortex%20current%20in%20a%20biased-ladder%20superfluid&amp;journal=Phys.%20Rev.%20Res.&amp;doi=10.1103%2FPhysRevResearch.6.013037&amp;volume=6&amp;publication_year=2024&amp;author=Huang%2CW&amp;author=Yao%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"61.\">\n<p class=\"c-article-references__text\" id=\"ref-CR61\">Wang, B., Dong, X.-Y., \u00dcnal, F. N. &amp; Eckardt, A. Robust and ultrafast state preparation by ramping artificial gauge potentials. New J. Phys. <b>23<\/b>, 063017 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/1367-2630\/abf9b2\" data-track-item_id=\"10.1088\/1367-2630\/abf9b2\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1367-2630%2Fabf9b2\" aria-label=\"Article reference 61\" data-doi=\"10.1088\/1367-2630\/abf9b2\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021NJPh...23f3017W\" aria-label=\"ADS reference 61\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 61\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Robust%20and%20ultrafast%20state%20preparation%20by%20ramping%20artificial%20gauge%20potentials&amp;journal=New%20J.%20Phys.&amp;doi=10.1088%2F1367-2630%2Fabf9b2&amp;volume=23&amp;publication_year=2021&amp;author=Wang%2CB&amp;author=Dong%2CX-Y&amp;author=%C3%9Cnal%2CFN&amp;author=Eckardt%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"62.\">\n<p class=\"c-article-references__text\" id=\"ref-CR62\">Schindler, P. M. &amp; Bukov, M. Counterdiabatic driving for periodically driven systems. Phys. Rev. Lett. <b>133<\/b>, 123402 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.133.123402\" data-track-item_id=\"10.1103\/PhysRevLett.133.123402\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.133.123402\" aria-label=\"Article reference 62\" data-doi=\"10.1103\/PhysRevLett.133.123402\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4806899\" aria-label=\"MathSciNet reference 62\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 62\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Counterdiabatic%20driving%20for%20periodically%20driven%20systems&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.133.123402&amp;volume=133&amp;publication_year=2024&amp;author=Schindler%2CPM&amp;author=Bukov%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"63.\">\n<p class=\"c-article-references__text\" id=\"ref-CR63\">Viebahn, K. et al. Suppressing dissipation in a Floquet-Hubbard system. Phys. Rev. X <b>11<\/b>, 011057 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 63\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Suppressing%20dissipation%20in%20a%20Floquet-Hubbard%20system&amp;journal=Phys.%20Rev.%20X&amp;volume=11&amp;publication_year=2021&amp;author=Viebahn%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"64.\">\n<p class=\"c-article-references__text\" id=\"ref-CR64\">Palm, F. A., Mardazad, S., Bohrdt, A., Schollw\u00f6ck, U. &amp; Grusdt, F. Snapshot-based detection of \ud835\udf08\u2009=\u20091\/2 Laughlin states: coupled chains and central charge. Phys. Rev. B <b>106<\/b>, L081108 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.106.L081108\" data-track-item_id=\"10.1103\/PhysRevB.106.L081108\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.106.L081108\" aria-label=\"Article reference 64\" data-doi=\"10.1103\/PhysRevB.106.L081108\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022PhRvB.106h1108P\" aria-label=\"ADS reference 64\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 64\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Snapshot-based%20detection%20of%20%F0%9D%9C%88%E2%80%89%3D%E2%80%891%2F2%20Laughlin%20states%3A%20coupled%20chains%20and%20central%20charge&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.106.L081108&amp;volume=106&amp;publication_year=2022&amp;author=Palm%2CFA&amp;author=Mardazad%2CS&amp;author=Bohrdt%2CA&amp;author=Schollw%C3%B6ck%2CU&amp;author=Grusdt%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"65.\">\n<p class=\"c-article-references__text\" id=\"ref-CR65\">Wang, B., Dong, X. &amp; Eckardt, A. Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope. SciPost Phys. <b>12<\/b>, 095 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.21468\/SciPostPhys.12.3.095\" data-track-item_id=\"10.21468\/SciPostPhys.12.3.095\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.21468%2FSciPostPhys.12.3.095\" aria-label=\"Article reference 65\" data-doi=\"10.21468\/SciPostPhys.12.3.095\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022ScPP...12...95W\" aria-label=\"ADS reference 65\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 65\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Measurable%20signatures%20of%20bosonic%20fractional%20Chern%20insulator%20states%20and%20their%20fractional%20excitations%20in%20a%20quantum-gas%20microscope&amp;journal=SciPost%20Phys.&amp;doi=10.21468%2FSciPostPhys.12.3.095&amp;volume=12&amp;publication_year=2022&amp;author=Wang%2CB&amp;author=Dong%2CX&amp;author=Eckardt%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n<li class=\"c-article-references__item js-c-reading-companion-references-item\" data-counter=\"66.\">\n<p class=\"c-article-references__text\" id=\"ref-CR66\">Palm, F. A., Repellin, C., Goldman, N. &amp; Grusdt, F. Absence of gapless Majorana edge modes in few-leg bosonic flux ladders. Phys. Rev. Res. <b>7<\/b>, L012001 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevResearch.7.L012001\" data-track-item_id=\"10.1103\/PhysRevResearch.7.L012001\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevResearch.7.L012001\" aria-label=\"Article reference 66\" data-doi=\"10.1103\/PhysRevResearch.7.L012001\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 66\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Absence%20of%20gapless%20Majorana%20edge%20modes%20in%20few-leg%20bosonic%20flux%20ladders&amp;journal=Phys.%20Rev.%20Res.&amp;doi=10.1103%2FPhysRevResearch.7.L012001&amp;volume=7&amp;publication_year=2025&amp;author=Palm%2CFA&amp;author=Repellin%2CC&amp;author=Goldman%2CN&amp;author=Grusdt%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<\/li>\n","protected":false},"excerpt":{"rendered":"Eckardt, A. Colloquium: atomic quantum gases in periodically driven optical lattices. Rev. Mod. Phys. 89, 011004 (2017). Article\u00a0&hellip;\n","protected":false},"author":2,"featured_media":72682,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3845],"tags":[11701,11700,11705,11704,3968,11699,11702,11703,74,15192,70,11698,31446,16,36134,15],"class_list":{"0":"post-72681","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-atomic","9":"tag-classical-and-continuum-physics","10":"tag-complex-systems","11":"tag-condensed-matter-physics","12":"tag-general","13":"tag-mathematical-and-computational-physics","14":"tag-molecular","15":"tag-optical-and-plasma-physics","16":"tag-physics","17":"tag-quantum-simulation","18":"tag-science","19":"tag-theoretical","20":"tag-topological-matter","21":"tag-uk","22":"tag-ultracold-gases","23":"tag-united-kingdom"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@uk\/114447137071583608","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/72681","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/comments?post=72681"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/72681\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/72682"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=72681"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=72681"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=72681"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}