• Luski, A. et al. Vortex beams of atoms and molecules. Science 373, 1105–1109 (2021).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Bardeen, J. & Stephen, M. J. Theory of the motion of vortices in superconductors. Phys. Rev. 140, A1197–A1207 (1965).

    Article 

    Google Scholar
     

  • Abrikosov, A. A. Nobel Lecture. Type-II superconductors and the vortex lattice. Rev. Mod. Phys. 76, 975–979 (2004).

    Article 
    CAS 

    Google Scholar
     

  • Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).

    Article 

    Google Scholar
     

  • Willner, A. E., Wang, J. & Huang, H. A different angle on light communications. Science 337, 655–656 (2012).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Abbott, B. P. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Kivshar, Y. S. Optical vortices and vortex solitons. In Proc. SPIE 5508, Complex Mediums V: Light and Complexity (eds McCall, M. W. & Dewar, G.) Vol. 16 (SPIE, 2004).

  • Matthews, M. R. et al. Vortices in a Bose–Einstein condensate. Phys. Rev. Lett. 83, 2498–2501 (1999).

    Article 
    CAS 

    Google Scholar
     

  • Zurek, W. H. Cosmological experiments in condensed matter systems. Phys. Rep. 276, 177–221 (1996).

    Article 
    CAS 

    Google Scholar
     

  • Bowick, M. J., Chandar, L., Schiff, E. A. & Srivastava, A. M. The cosmological Kibble mechanism in the laboratory: string formation in liquid crystals. Science 263, 943–945 (1994).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Wen, X.-G. Choreographed entanglement dances: topological states of quantum matter. Science 363, eaal3099 (2019).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Kibble, T. W. B. Topology of cosmic domains and strings. J. Phys. Math. Gen. 9, 1387–1398 (1976).

    Article 

    Google Scholar
     

  • Yao, K.-X., Zhang, Z. & Chin, C. Domain-wall dynamics in Bose–Einstein condensates with synthetic gauge fields. Nature 602, 68–72 (2022).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Schoenherr, P. et al. Topological domain walls in helimagnets. Nat. Phys. 14, 465–468 (2018).

    Article 
    CAS 

    Google Scholar
     

  • Mermin, N. D. The topological theory of defects in ordered media. Rev. Mod. Phys. 51, 591–648 (1979).

    Article 
    CAS 

    Google Scholar
     

  • Rodrigues, D. R., Abanov, A. R., Sinova, J. & Everschor-Sitte, K. Effective description of domain wall strings. Phys. Rev. B 97, 134414 (2018).

    Article 
    CAS 

    Google Scholar
     

  • Carlon Zambon, N. et al. Optically controlling the emission chirality of microlasers. Nat. Photonics 13, 283–288 (2019).

    Article 
    CAS 

    Google Scholar
     

  • Sala, V. G. et al. Spin–orbit coupling for photons and polaritons in microstructures. Phys. Rev. X 5, 011034 (2015).


    Google Scholar
     

  • Lagoudakis, K. G. et al. Quantized vortices in an exciton–polariton condensate. Nat. Phys. 4, 706–710 (2008).

    Article 
    CAS 

    Google Scholar
     

  • Dominici, L. et al. Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid. Sci. Adv. 1, e1500807 (2015).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Liu, G., Snoke, D. W., Daley, A., Pfeiffer, L. N. & West, K. A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate. Proc. Natl Acad. Sci. USA 112, 2676–2681 (2015).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Manni, F., Léger, Y., Rubo, Y. G., André, R. & Deveaud, B. Hyperbolic spin vortices and textures in exciton–polariton condensates. Nat. Commun. 4, 2590 (2013).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Borgh, M. O., Keeling, J. & Berloff, N. G. Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate. Phys. Rev. B 81, 235302 (2010).

    Article 

    Google Scholar
     

  • Caputo, D. et al. Topological order and thermal equilibrium in polariton condensates. Nat. Mater. 17, 145–151 (2018).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Pavlovic, G., Malpuech, G. & Shelykh, I. A. Pseudospin dynamics in multimode polaritonic Josephson junctions. Phys. Rev. B 87, 125307 (2013).

    Article 

    Google Scholar
     

  • Roumpos, G. et al. Single vortex–antivortex pair in an exciton-polariton condensate. Nat. Phys. 7, 129–133 (2011).

    Article 
    CAS 

    Google Scholar
     

  • Pickup, L., Töpfer, J. D., Sigurdsson, H. & Lagoudakis, P. G. Polariton spin jets through optical control. Phys. Rev. B 103, 155302 (2021).

    Article 
    CAS 

    Google Scholar
     

  • Gnusov, I. et al. Quantum vortex formation in the ‘rotating bucket’ experiment with polariton condensates. Sci. Adv. 9, eadd1299 (2023).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Li, Y. et al. Manipulating polariton condensates by Rashba–Dresselhaus coupling at room temperature. Nat. Commun. 13, 3785 (2022).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Łempicka-Mirek, K. et al. Electrically tunable Berry curvature and strong light-matter coupling in liquid crystal microcavities with 2D perovskite. Sci. Adv. 8, eabq7533 (2022).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Liang, J. et al. Polariton spin Hall effect in a Rashba–Dresselhaus regime at room temperature. Nat. Photonics 18, 357–362 (2024).

    Article 
    CAS 

    Google Scholar
     

  • Zhai, X. et al. Electrically controlling vortices in a neutral exciton polariton condensate at room temperature. Phys. Rev. Lett. 131, 136901 (2023).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Zhai, X. et al. Observation of spin–orbit coupled polariton vortices at room temperature. Nano Lett. 26, 4402–4409 (2026).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Caputo, D. et al. Magnetic control of polariton spin transport. Commun. Phys. 2, 165 (2019).

    Article 

    Google Scholar
     

  • Dufferwiel, S. et al. Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting. Phys. Rev. Lett. 115, 246401 (2015).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Tao, R. et al. Halide perovskites enable polaritonic XY spin Hamiltonian at room temperature. Nat. Mater. 21, 761–766 (2022).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Caputo, D. et al. Josephson vortices induced by phase twisting a polariton superfluid. Nat. Photonics 13, 488–493 (2019).

    Article 
    CAS 

    Google Scholar
     

  • Manni, F. et al. Dissociation dynamics of singly charged vortices into half-quantum vortex pairs. Nat. Commun. 3, 1309 (2012).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Dominici, L. et al. Coupled quantum vortex kinematics and Berry curvature in real space. Commun. Phys. 6, 197 (2023).

    Article 

    Google Scholar
     

  • Dang, N. H. M. et al. Long-range ballistic propagation of 80% excitonic fraction polaritons in a Perovskite metasurface at room temperature. Nano Lett. 24, 11839–11846 (2024).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Ardizzone, V. et al. Polariton Bose–Einstein condensate from a bound state in the continuum. Nature 605, 447–452 (2022).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Hsu, C. W., Zhen, B., Stone, A. D., Joannopoulos, J. D. & Soljačić, M. Bound states in the continuum. Nat. Rev. Mater. 1, 16048 (2016).

    Article 
    CAS 

    Google Scholar
     

  • Koshelev, K. L., Sadrieva, Z. F., Shcherbakov, A. A., Kivshar, Y.uS. & Bogdanov, A. A. Bound states in the continuum in photonic structures. Phys.Usp. 66, 494–517 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Zhen, B., Hsu, C. W., Lu, L., Stone, A. D. & Soljačić, M. Topological nature of optical bound states in the continuum. Phys. Rev. Lett. 113, 257401 (2014).

    Article 
    PubMed 

    Google Scholar
     

  • Tian, J. et al. Optical Rashba effect in a light-emitting perovskite metasurface. Adv. Mater. 34, 2109157 (2022).

    Article 
    CAS 

    Google Scholar
     

  • Tian, J. et al. Phase-change perovskite microlaser with tunable polarization vortex. Adv. Mater. 35, 2207430 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Wang, Y. et al. Directional emission from electrically injected exciton–polaritons in perovskite metasurfaces. Nano Lett. 23, 4431–4438 (2023).

    Article 
    PubMed 

    Google Scholar
     

  • Dang, N. H. M. et al. Realization of polaritonic topological charge at room temperature using polariton bound states in the continuum from perovskite metasurface. Adv. Opt. Mater. 10, 2102386 (2022).

    Article 
    CAS 

    Google Scholar
     

  • Peng, K. et al. Room-temperature polariton quantum fluids in halide perovskites. Nat. Commun. 13, 7388 (2022).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Wu, X. et al. Exciton polariton condensation from bound states in the continuum at room temperature. Nat. Commun. 15, 3345 (2024).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Wang, Y., Adamo, G., Ha, S. T., Tian, J. & Soci, C. Electrically generated exciton polaritons with spin on-demand. Adv. Mater. 37, 2412952 (2025).

    Article 
    CAS 

    Google Scholar
     

  • Meng, Y. et al. Hybrid perovskite–nanograting photonic architecture enables supersolidity at room temperature. Nat. Nanotechnol. 21, 663–671 (2026).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Volovik, G. E. The Universe in a Helium Droplet (Oxford Univ. Press, 2009).

  • Liu, W. et al. Circularly polarized states spawning from bound states in the continuum. Phys. Rev. Lett. 123, 116104 (2019).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Liu, W. et al. Exploiting topological darkness in photonic crystal slabs for spatiotemporal vortex generation. Nano Lett. 24, 943–949 (2024).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Marangi, M., Zacheo, A., Dubrovkin, A. M., Adamo, G. & Soci, C. Exciton–polariton condensation in MAPbI3 films from bound states in the continuum metasurfaces. Nanophotonics 14, 4241–4247 (2025).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Masharin, M. A. et al. Room-temperature exceptional-point-driven polariton lasing from perovskite metasurface. Adv. Funct. Mater. 33, 2215007 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Chestnov, I. et al. Stimulated exciton–polariton scattering in hybrid halide perovskites. ACS Photonics 12, 801–808 (2025).

    Article 
    CAS 

    Google Scholar
     

  • Rubo, Y. G. Half vortices in exciton polariton condensates. Phys. Rev. Lett. 99, 106401 (2007).

    Article 
    PubMed 

    Google Scholar
     

  • Lagoudakis, K. G. et al. Observation of half-quantum vortices in an exciton-polariton condensate. Science 326, 974–976 (2009).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Toledo-Solano, M., Mora-Ramos, M. E., Figueroa, A. & Rubo, Y. G. Warping and interactions of vortices in exciton-polariton condensates. Phys. Rev. B 89, 035308 (2014).

    Article 

    Google Scholar
     

  • Flayac, H., Shelykh, I. A., Solnyshkov, D. D. & Malpuech, G. Topological stability of the half-vortices in spinor exciton-polariton condensates. Phys. Rev. B 81, 045318 (2010).

    Article 

    Google Scholar
     

  • Van Straten, W., Manchester, R. N., Johnston, S. & Reynolds, J. E. psrchive and psrfits: definition of the Stokes parameters and instrumental basis conventions. Publ. Astron. Soc. Aust. 27, 104–109 (2010).

    Article 

    Google Scholar
     

  • Gippius, N. A. et al. Polarization multistability of cavity polaritons. Phys. Rev. Lett. 98, 236401 (2007).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Vladimirova, M. et al. Polariton–polariton interaction constants in microcavities. Phys. Rev. B 82, 075301 (2010).

    Article 

    Google Scholar
     

  • Dominici, L. et al. Interactions and scattering of quantum vortices in a polariton fluid. Nat. Commun. 9, 1467 (2018).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Mäkinen, J. T. et al. Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid 3He. Nat. Commun. 10, 237 (2019).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Salomaa, M. M. & Volovik, G. E. Quantized vortices in superfluid He 3. Rev. Mod. Phys. 59, 533–613 (1987).

    Article 
    CAS 

    Google Scholar
     

  • Solano, M. T. & Rubo, Y. G. Vortices in exciton-polariton condensates with polarization splitting. J. Phys. Conf. Ser. 210, 012024 (2010).

    Article 

    Google Scholar
     

  • Kavokin, A., Malpuech, G. & Glazov, M. Optical spin Hall effect. Phys. Rev. Lett. 95, 136601 (2005).

    Article 
    PubMed 

    Google Scholar
     

  • Rao, L. et al. Meron spin textures in momentum space spawning from bound states in the continuum. Phys. Rev. Lett. 135, 026203 (2025).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Liew, T. C. H., Rubo, Y. G. & Kavokin, A. V. Generation and dynamics of vortex lattices in coherent exciton-polariton fields. Phys. Rev. Lett. 101, 187401 (2008).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Hu, J. et al. Vortex molecules in exciton-polariton condensates formed by uniform nonresonant pumping. Phys. Rev. B 111, 245119 (2025).

    Article 
    CAS 

    Google Scholar
     

  • Kavokin, A. et al. Polariton condensates for classical and quantum computing. Nat. Rev. Phys. 4, 435–451 (2022).

    Article 

    Google Scholar
     

  • Ballarini, D. et al. All-optical polariton transistor. Nat. Commun. 4, 1778 (2013).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Berry, H. G., Gabrielse, G. & Livingston, A. E. Measurement of the Stokes parameters of light. Appl. Opt. 16, 3200 (1977).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Tyo, J. S. Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error. Appl. Opt. 41, 619 (2002).

    Article 
    PubMed 

    Google Scholar