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arXiv:2507.14585

Supersolidity in Optically Trapped Polariton Condensates

Pavel Kozhevin, A. D. Liubomirov, R. V. Cherbunin, M. A. Chukeev, Igor Yu. Chestnov, Alexey Vitalievich Kavokin, Anton V. Nalitov

Published Jul 19, 2025• 0 citations
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Abstract

Superfluids under specific conditions can exhibit spontaneous breaking of continuous translation symmetries and form exotic spatially ordered states of matter known as supersolids. Despite its early theoretical prediction, it took over half-a-centrury to experimentally demonstrate the supersolid phase in ultracold atomic Bose-Einstein condensates, forming due to long-range interatomic interactions. Here we propose as a promising new platform for supersolidity exciton-polariton superfluids, confined in annular optically induced traps. The supersolid phase emerges due to effective attractive interactions, mediated by the normal excitonic component of the system. Experimental demonstration of spontaneously formed spatially ordered phase is in agreement with detailed mean-field theoretical analysis and numerical simulation. The spontaneous character of the observed supersolid transition is further evidenced by the formation of specific zero-energy Nambu-Goldstone modes in the collective excitation spectrum.

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Superfluids under specific conditions can exhibit spontaneous breaking of continuous translation symmetries and form exotic spatially ordered states of matter known as supersolids. Despite its early theoretical prediction, it took over half-a-centrury to experimentally demonstrate the supersolid phase in ultracold atomic Bose-Einstein condensates, forming due to long-range interatomic interactions. Here we propose as a promising new platform for supersolidity exciton-polariton superfluids, confined in annular optically induced traps. The supersolid phase emerges due to effective attractive interactions, mediated by the normal excitonic component of the system. Experimental demonstration of spontaneously formed spatially ordered phase is in agreement with detailed mean-field theoretical analysis and numerical simulation. The spontaneous character of the observed supersolid transition is further evidenced by the formation of specific zero-energy Nambu-Goldstone modes in the collective excitation spectrum.
Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of nonlinear dynamical phenomena.As a prominent example, particles can spontaneously form stationary periodic configurations that simultaneously maximize the light scattering and minimize the atomic potential energy in the emerging optical lattice.Such self-ordering effects resulting in periodic lattices via bimodal symmetry breaking have been experimentally observed with cold gases and Bose-Einstein condensates (BECs) inside an optical resonator.Here, we study a new regime of periodic pattern formation for an atomic BEC in free space, driven by far off-resonant counterpropagating and noninterfering lasers of orthogonal polarization.In contrast to previous works, no spatial light modes are preselected by any boundary conditions and the transition from homogeneous to periodic order amounts to a crystallization of both light and ultracold atoms breaking a continuous translational symmetry.In the crystallized state the BEC acquires a phase similar to a supersolid with an emergent intrinsic length scale whereas the light field forms an optical lattice allowing phononic excitations via collective backscattering, which are gapped due to the infinte-range interactions.The system we study constitutes a novel configuration allowing the simulation of synthetic solid-state systems with ultracold atoms including long-range phonon dynamics.
The supersolid phase characterized by the superfluid and long-range spatial periodicity of crystalline order is central to many branches of science ranging from condensed matter physics to ultracold atomic physics. Here we study a self-ordered checkerboard supersolid phase originating from dynamical spin-orbit coupling for a transversely pumped atomic Bose-Einstein condensate trapped in a ring cavity, corresponding to a superradiant anti-Tavis-Cummings phase transition. In particular, an undamped gapless Goldstone mode is observed in contrast to the experimentally realized lattice supersolid with a gapped roton mode for Dicke superradiance. This zero-energy mode reveals the rigidity of the self-ordered superradiant phase, which spontaneously breaks a continuous translational symmetry. Our work will highlight the significant opportunities for exploring long-lived supersolid matter by utilizing dynamical spin-orbit coupling in controllable optical cavities.
In Bose-Einstein condensates (BEC), spin-orbit coupling (SOC) produces supersolidity. It is a peculiar state of matter, which, in addition to the superfluid behaviour shows periodic density modulation typical for crystals. Here, we report the fabrication of a new type of optical microcavity allowing to achieve room-temperature supersolidity for a quantum fluid of light. The microcavity is filled with a nematic liquid crystal (LC) and two layers of the organic polymer MeLPPP hosting exciton resonances. We demonstrate exciton-polariton condensation in the two distinct degenerate minima of the dispersion created by the LC induced Rashba-Dresselhaus (RD) SOC. The condensate real-space distribution shows density stripes located randomly from one condensate realization to another despite the presence of a random disorder potential. This demonstrates the immunity of stripes against disorder (that is, superfluidity) and the spontaneous breaking of translational invariance. We also report the random appearance of vortices via the Kibble-Zurek mechanism, another smoking gun of superfluidity.
Motivated by a recent experiment [L. Chomaz et al., Nat. Phys. 14, 442 (2018)], we perform numerical simulations of a dipolar Bose-Einstein condensate (BEC) in a tubular, periodic confinement at T=0T=0T=0 within density functional theory, where the beyond-mean-field correction to the ground-state energy is included in the local density approximation. We study the excitation spectrum of the system by solving the corresponding Bogoliubov--de Gennes equations. The calculated spectrum shows a roton minimum, and the roton gap decreases by reducing the effective scattering length. As the roton gap disappears, the system spontaneously develops a periodic linear structure formed by denser clusters of atomic dipoles immersed in a dilute superfluid background. This structure shows the hallmarks of a supersolid system, i.e., (i) a finite nonclassical translational inertia along the tube axis and (ii) the appearance of two gapless modes, i.e., a phonon mode associated with density fluctuations and resulting from the translational discrete symmetry of the system, and a Nambu-Goldstone gapless mode corresponding to phase fluctuations, resulting from the spontaneous breaking of the gauge symmetry. A further decrease in the scattering length eventually leads to the formation of a periodic linear array of self-bound droplets.
In Bose-Einstein condensates, spin-orbit coupling (SOC) produces supersolidity. It is a peculiar state of matter, which, in addition to the superfluid behavior, shows periodic density modulation typical for crystals. Here, we report the fabrication of an original type of optical microcavity, allowing the achievement of room-temperature supersolidity for a quantum fluid of light. The microcavity is filled with a nematic liquid crystal (LC) and two layers of the organic polymer methyl-substituted ladder-type poly( p -phenylene) (MeLPPP) hosting exciton resonances. We demonstrate exciton-polariton condensation in the two distinct degenerate minima of the dispersion created by the LC-induced Rashba-Dresselhaus SOC. The condensate real-space distribution shows density stripes located randomly from one condensate realization to another despite the presence of a random disorder potential. This demonstrates the immunity of stripes against disorder and the spontaneous breaking of translational invariance. We also report the random appearance of vortices, another feature of superfluids.
Supersolidity is deeply connected with the emergence of Goldstone modes, reflecting the spontaneous breaking of both phase and translational symmetry. Here, we propose accessible signatures of these modes in harmonically trapped spin-orbit-coupled Bose-Einstein condensates, where supersolidity appears in the form of stripes. By suddenly changing the trapping frequency, an axial breathing oscillation is generated, whose behavior changes drastically at the critical Raman coupling. Above the transition, a single mode of hybridized density and spin nature is excited, while below it, we predict a beating effect signaling the excitation of a Goldstone spin-dipole mode. We further provide evidence for the Goldstone mode associated with the translational motion of stripes. Our results open up new perspectives for probing supersolid properties in experimentally relevant configurations with both symmetric as well as highly asymmetric intraspecies interactions.