{"id":452280,"date":"2026-04-24T22:24:20","date_gmt":"2026-04-24T22:24:20","guid":{"rendered":"https:\/\/www.europesays.com\/ie\/452280\/"},"modified":"2026-04-24T22:24:20","modified_gmt":"2026-04-24T22:24:20","slug":"cavity-mediated-exciton-hopping-in-a-dielectrically-engineered-polariton-system","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/ie\/452280\/","title":{"rendered":"Cavity-mediated exciton hopping in a dielectrically engineered polariton system"},"content":{"rendered":"

Our approach, illustrated schematically in Fig.\u00a01<\/a>a, is based on a van der Waals heterostack with a monolayer of molybdenum diselenide (MoSe2) encapsulated by a planar bottom hBN layer and a patterned top hBN layer with through-holes defined by reactive-ion etching (see the \u201cMethods\u201d section for details). The resulting modification of the dielectric environment on the scale of a few hundred of nanometers affects both the monolayer band gap and the exciton binding energy14<\/a>,15<\/a>,17<\/a>, yielding a spatially modified exciton resonance energy which in turn determines local properties of exciton-polaritons upon strong coupling to an optical microcavity with photonic modes confined in all spatial directions. The left panel in Fig.\u00a01<\/a>b shows an optical micrograph of the corresponding sample, with two holes in the top hBN layer of same diameter and variable distance as pairs of yellow circles. The right panel illustrates schematically the resulting exciton landscape: left (L) and right (R) disk-shaped exciton domains at each etch site are surrounded by monolayer excitons (X) in the unpatterned area. Due to fabrication imperfections such as interfacial bubbles and unintentional strain, the exciton energies EL and ER differ between the two nominally identical domains, and both differ from the surrounding exciton energy EX by virtue of different dielectric environments.<\/p>\n

Fig. 1: Dielectric engineering of polariton domains.<\/b>\"Fig.The alternative text for this image may have been generated using AI.<\/p>\n

a<\/b> Schematics of a MoSe2 monolayer encapsulated by planar bottom and patterned top hBN layers with spatially distinct regions of exciton-polaritons formed by strong coupling to the mode of an open cavity. b<\/b> Left panel: optical micrograph of the van der Waals heterostructure, with pairs of holes in the top hBN layer P1, P2, and P3 visible as yellow circles of nominally identical left (L) and right (R) disks with variable separation, surrounded by fully encapsulated monolayer. The scale bar is 2\u2009\u03bcm. Right panel: The red dashed circle shows the waist diameter of the cavity mode on the scale of the diameters and distances of disk-shaped domains surrounded by regions of monolayer excitons (X) in unpatterned hBN. c<\/b> Schematic of the cryogenic fiber-based open microcavity, with piezoelectrically actuated lateral translation in the x\u00a0\u2212\u00a0y plane and cavity length (LC) tuning along z. d<\/b> Cavity transmission as a function of the cavity length tuned via the z-piezo voltage, recorded away from structured hBN. The cavity energy corresponding to each length index is indicated on the upper horizontal axis. The exciton energy EX is indicated by the horizontal solid line. e<\/b> Same but with the cavity mode positioned near the center of a single exciton disk of etched pair P2 as illustrated in the inset. The solid horizontal lines indicate the energy of monolayer and disk-localized excitons EX and EL, respectively.<\/p>\n

In the following, we focus on three etch-site pairs P1, P2 and P3 in Fig.\u00a01<\/a>b with 2.0, 1.4 and 1.1\u2009\u03bcm distances between the centers of the left and right holes with identical diameters of 0.6\u2009\u03bcm. The finite extent of the fundamental Gaussian cavity mode with a waist of ~1\u03bcm (shown by the red dashed circle in the schematics of Fig.\u00a01<\/a>b) and the tunability of the resonance energy as well as the lateral mode position of our open cavity (as indicated in Fig.\u00a01<\/a>c) allow us to study different limits of polaritons in strong light-matter coupling. First, by placing the cavity mode over the left site of the pair P1 or P2 that is sufficiently distant from its right counterpart, we study the local formation of polaritons in the left disk as well as their coupling to the surrounding exciton-polariton continuum (top panel of the schematics in Fig.\u00a01<\/a>b). In the second setting (central panel in Fig.\u00a01<\/a>b), the cavity mode creates and samples both left and right polariton disks, yet at a distance too large for intersite coupling. The third configuration (bottom panel in Fig.\u00a01<\/a>b), finally, is used to demonstrate effective cavity-mediated coupling between the left and right sites of polariton pairs.<\/p>\n

We begin by calibrating the coupling strength between the exciton domains and our tunable microcavity in a closed-cycle cryostat with a base temperature of 4.3\u2009K28<\/a> according to the schematics in Fig.\u00a01<\/a>c (see the \u201cMethods\u201d section for details on the cavity setup). The nanopatterned heterostack is placed on a macroscopic planar mirror, whose vertical separation LC from the microscopic mirror of the micromachined fiber facet is controlled by piezoelectric actuators, which also allow for lateral displacement of the sample with respect to the cavity mode. As such, the spectral resonance condition between the exciton and cavity energy, EX and EC, is tunable via the cavity length and exhibits a clear signature of strong-coupling in the cavity transmission of Fig.\u00a01<\/a>d on a region away from structured hBN. The avoided crossing is a hallmark of polariton formation, with light-matter coupling strength gX\u00a0=\u00a09.6\u2009meV at longitudinal cavity mode order q\u00a0=\u00a06 as determined from the dissipative model analysis (see Supplementary Note\u00a0II<\/a> for details). This coupling strength is characteristic for cavity-coupling of monolayer excitons28<\/a>,29<\/a>, and places the system together with polariton linewidths of ~2.5\u2009meV and the cavity linewidth \u03ba\u22431.5\u2009meV (limited by residual vibrational fluctuations in the cavity length28<\/a>) in the regime of strong light-matter coupling30<\/a>.<\/p>\n

We observe a strong modification of the characteristic exciton-polariton splitting as we position the cavity over the left hole-etched site of P2, with cavity transmission shown in Fig.\u00a01<\/a>e. As a function of the cavity length detuning, we observe an additional polariton branch related to the disk-localized exciton fraction with energy EL, redshifted from EX by 10\u2009meV due to effectively reduced screening below the hole in hBN. As the area of the local exciton domain is smaller than the cavity spot, the corresponding light-matter coupling strength is reduced to gL\u00a0=\u00a02.65\u00a0\u00b1\u00a00.04\u2009meV as compared to the coupling of spatially unconfined monolayer excitons in regions with both-sided hBN encapsulation (see Supplementary Note\u00a0III<\/a> for details). This scaling of the light-matter coupling with the spatial extent of exciton-confining domains with redshifted transition energy indicates the formation of local polariton disks.<\/p>\n

The creation of exciton domains results in local shifts of the polariton energy, which we map out by spatial and spectral cavity tuning with data shown in Fig.\u00a02<\/a>. Displacing the cavity laterally at a constant cavity length across one domain of the pair P1, the cavity transmission leads to the evolution of the upper and lower polariton branches as in Fig.\u00a02<\/a>a. In agreement with the data in Fig.\u00a01<\/a>e, the middle polariton branch is visible at an energy of ~1.640\u2009eV. The intensity of this feature is brightened as a result of spectral overlap with higher order transverse cavity modes (see Supplementary Note\u00a0II<\/a> for details). Crucially, the lower polariton branch exhibits an energetic minimum at the center of the etch site. We emphasize that this redshift of ~2\u2009meV would correspond to an attractive polariton potential for spatially extended polaritons in two-dimensional cavities31<\/a>, thereby providing lateral confinement for exciton-polaritons. The superimposed near-linear energy gradient, also evidenced in the upper polariton branch, stems from the unintentional spatial gradient of the exciton energy EX around this site.<\/p>\n

Fig. 2: Dielectrically engineered polariton disks with cavity-controlled local energy modulation.<\/b>\"Fig.The alternative text for this image may have been generated using AI.<\/p>\n

a<\/b> Cavity transmission for a fixed cavity energy and lateral cavity mode translation across the right exciton domain of pair P1, as illustrated in the inset. The cavity energy corresponds to an exciton-cavity detuning \u0394X\u00a0=\u00a0\u22125\u2009meV at position x\u00a0=\u00a0\u22121.2\u2009\u03bcm. The white solid lines show best fits of polynomial and Gaussian profiles to maximum transmission of the upper and lower polariton branches, respectively. b<\/b> Same but for the domain pair P2, recorded at similar detuning of\u00a0\u0394X\u00a0=\u00a0\u22127\u2009meV at x\u00a0=\u00a0\u22122.2\u2009\u03bcm (x\u00a0=\u00a00\u2009\u03bcm corresponds to the cavity mode positioned in between the two exciton disks, as illustrated in the inset). The dashed lines are the individual Gaussian contributions to the full lower polariton transmission profile shown by the solid line. The spectra at each position were normalized to the maximum transmission of the lower polariton branch and rescaled for the upper polariton branch by a factor of 0.8 and 0.2 as indicated in the respective sub-panels. c<\/b> Lower polariton energy shift \u0394ELP as a function of the cavity energy, defined as illustrated in (d<\/b>) for the right polariton disk of P2. d<\/b> Energy profiles of the lower polaritons (corresponding to the transmission maxima in (b<\/b>) as a function of the lateral cavity displacement for five cavity energies indicated by the color-bar. The solid lines show best fits of two Gaussians to the polariton energy profiles at different cavity energies.<\/p>\n

The effect of the nanostructured dielectric environment on the polariton energy is even richer in the pair P2 with transmission data in Fig.\u00a02<\/a>b. Upon spatial displacement across the left and right disk of the pair for a constant cavity energy, we observe in Fig.\u00a02<\/a>b two local energy minima for the lower polariton branch, indicated by the two Gaussian contributions (dashed lines) to the full transmission profile (solid line). The difference in the left and right local energy shift is related to differences in the disks from imperfect fabrication. Remarkably, the energy shift \u0394ELP is tunable via the cavity energy, as evident from the dependence of the lower polariton energies on the cavity energy shown for five discrete values in Fig.\u00a02<\/a>d. A systematic study of the lower polariton energy shift, shown in Fig.\u00a02<\/a>c, reveals a monotonous increase in \u0394ELP with increasing cavity energy, spanning a range of several meV.<\/p>\n

The dependence of \u0394ELP on the cavity resonance condition can be understood by noting that for large cavity energy, the lowest polariton energy in the system is dictated by the lowest-energy exciton. By virtue of dielectric engineering, the exciton energy at the etch-site center is reduced from its monolayer value in fully hBN-encapsulated regions. Thus, in the limit of large cavity energies, the local energy shift for the lower polariton corresponds to the energy difference imprinted by different dielectric environments.<\/p>\n

The second key feature of our system is the ability to establish site-to-surrounding and site-to-site coupling in the dispersive cavity regime, mediating an effective long-range hopping. From a theoretical perspective, this coupling follows from the time-independent Hamiltonian for multiple cavity-coupled exciton domains i with light-matter coupling strengths gi, energies Ei and detunings \u0394i\u00a0=\u00a0Ei\u00a0\u2212\u00a0EC from the cavity energy EC. Expansion to second order in gi\/\u0394i via a Schrieffer-Wolff transformation23<\/a>,24<\/a> yields: <\/p>\n

$$H\\simeq \\left({E}_{C}-{\\sum }_{i}\\frac{{g}_{i}^{2}}{{\\Delta }_{i}}\\right){a}^{{{\\dagger}} }a+{\\sum }_{i}\\left({E}_{i}+\\frac{{g}_{i}^{2}}{{\\Delta }_{i}}\\right){b}_{i}^{{{\\dagger}} }{b}_{i}+{\\sum }_{i}{\\sum }_{j\\ne i}\\frac{{g}_{i}{g}_{j}}{2{\\Delta }_{i}}\\left({b}_{i}^{{{\\dagger}} }{b}_{j}+{b}_{j}^{{{\\dagger}} }{b}_{i}\\right),$$<\/p>\n

\n (1)\n <\/p>\n

with the respective bosonic annihilation operators for cavity photons and excitons, a and bi. The result is a system described by multiple exciton resonances which are weakly dressed by cavity photons, evidenced by the diagonal first and second terms of Eq. (1<\/a>). In addition, excitons associated with different resonances i and j are coupled via an effective beam-splitter type coupling of strength \\({J}_{ij}={g}_{i}{g}_{j}\\left({\\Delta }_{i}^{-1}+{\\Delta }_{j}^{-1}\\right)\/2\\) as described by the third term of Eq. (1<\/a>), mediated by dispersive exchange of cavity photons.<\/p>\n

The resulting effective coupling between disk-localized excitons and their surrounding monolayer excitons is sizable when the cavity mode is positioned close to the edge of a single etch site. This effect is shown conceptually in Fig.\u00a03<\/a>a: since the light-matter coupling strength of X excitons greatly exceeds that of R and L domains, the dispersive shift of magnitude \\({g}_{i}^{2}\/{\\Delta }_{i}\\) (see Eq. (1<\/a>)) can be used to tune the difference in the respective energies of the bare excitons (left panel) into resonance (central panel). Here, dispersive coupling induces an effective splitting given by 2JLX (right panel). The corresponding experiment on the left disk in pair P2 shows in Fig.\u00a03<\/a>b the avoided crossing due to dispersive cavity-dressing and coupling, with a maximum coupling strength of 2JLX\u00a0=\u00a01.5\u2009meV for optimal conditions. In this regime, the eigenstates of the system derive from the Hamiltonian of Eq. (1<\/a>), with energies shown by the black dashed lines in the right panel of Fig.\u00a03<\/a>b (see Supplementary Note\u00a0V<\/a> for details). Unavoidably, the coupling vanishes as the cavity is moved away from the etch-site, as confirmed in Fig.\u00a03<\/a>c.<\/p>\n

Fig. 3: Cavity-mediated long-range effective exciton hopping.<\/b>\"Fig.The alternative text for this image may have been generated using AI.<\/p>\n

a<\/b> Top: Schematic of excitons L and X, coupled via an effective cavity-mediated hopping of strength JXL. Bottom left: exciton energies in the absence of a cavity mode. Bottom center: exciton energies tuned into resonance due to dispersive cavity-dressing of each individual exciton state. Bottom right: Exciton-like system eigenstates as observed in experiment, split due to the effective interaction JXL. b<\/b> Left panel: cavity transmission as a function of cavity energy, with the cavity mode positioned at the edge of the domain L as illustrated in the inset. Right panel: derivative of cavity transmission with respect to energy, computed for data in the dashed rectangle in the left panel. The black dashed lines are the eigenstates of the effective system Hamiltonian, Eq. (1<\/a>). The gray and orange lines are eigenstates of the Hamiltonian in the absence of hopping, JXL\u00a0=\u00a00, corresponding to energies of cavity-dressed but uncoupled X and L excitons, respectively. c<\/b> JXL as a function of the cavity mode position, which is moved away from the etch site center (x\u00a0=\u00a00\u2009\u03bcm corresponds to the mode position illustrated in the inset).<\/p>\n

Finally, we demonstrate effective long-range coupling mediated by the cavity between excitons of two distant sites, as shown conceptually in Fig.\u00a04<\/a>a: we use cavity-dressing to tune the energy of surrounding excitons X close to the resonances of the disks L and R. With dispersive coupling, we obtain hybrid eigenstates S1, S2 and S3 of the coupled system, with energies defined by effective interactions JXL, JXR and JLR among all three constituents. The corresponding spectral signature is shown in Fig.\u00a04<\/a>b, with maximal intersite coupling strength 2JLR of ~0.1\u2009meV and 1\u2009meV obtained for the pairs P2 and P3, respectively. In the framework of dispersive cavity-coupling, the\u00a0energies of the exciton-like hybrid eigenstates\u00a0differ from the bare exciton resonances\u00a0of the system as a direct result of the cavity-induced interaction. This observation is enabled by two features of our system: the energy difference of L and R excitons, a result of our choice of cavity mode position and sample inhomogeneities, renders all three eigenstates optically bright, while the tunability of our fiber cavity provides access to the relevant cavity energy. Lateral displacement of the cavity mode results in the reduction of coupling strength, as expected from Eq. (1<\/a>) and evidenced by the values for JXL as calculated from exciton energies and light-matter coupling strengths in Fig.\u00a04<\/a>c.<\/p>\n

Fig. 4: Effective inter-site and site-to-surrounding hopping.<\/b>\"Fig.The alternative text for this image may have been generated using AI.<\/p>\n

a<\/b> Coupling JLR between excitons of left and right domain L and R, mediated by the cavity in addition to the respective couplings JXL and JXR with the surrounding exciton reservoir X. b<\/b> Cavity transmission spectrum (dark green data) for a cavity energy of 1.659\u2009eV and mode position as illustrated in the inset with best fit (black solid line) according to the dissipative model analysis. The vertical lines indicate the eigenenergies of the coupled system. c<\/b> Coupling strength JLR at cavity energy 1.670\u2009eV for the etch site pairs P2 and P3 (black and dark green data, respectively, with error bars of one standard deviation and Gaussian fits as solid lines) as the cavity is moved across the etch site pair, as obtained from exciton light-matter coupling strengths and resonance energies (see Supplementary Note\u00a0V<\/a> for details). x\u00a0=\u00a00\u2009\u03bcm corresponds to the cavity mode centered between both sites. Error bars indicate one standard error, which for the site P2 is smaller than the respective data points.<\/p>\n","protected":false},"excerpt":{"rendered":"Our approach, illustrated schematically in Fig.\u00a01a, is based on a van der Waals heterostack with a monolayer of…\n","protected":false},"author":2,"featured_media":452281,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_share_on_mastodon":"0"},"categories":[271],"tags":[18,1099,19,17,139005,1100,452,133,9290],"class_list":["post-452280","post","type-post","status-publish","format-standard","has-post-thumbnail","category-physics","tag-eire","tag-humanities-and-social-sciences","tag-ie","tag-ireland","tag-microresonators","tag-multidisciplinary","tag-physics","tag-science","tag-two-dimensional-materials"],"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@ie\/116462031569596337","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/posts\/452280","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/comments?post=452280"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/posts\/452280\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/media\/452281"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/media?parent=452280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/categories?post=452280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/tags?post=452280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}