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Science Advances

Observation of a supersolid phase in a spin-orbit coupled exciton-polariton Bose-Einstein condensate

Marcin Muszyński, Pavel Kokhanchik, Rafał Mirek, Darius Urbonas, Pietro Tassan, Piotr Kapuściński, Przemysław Oliwa, Ioannis Georgakilas, Thilo Stöferle, Rainer F. Mahrt, Michael Förster, Ullrich Scherf, Dmitriy S. Dovzhenko, Rafał Mazur, Przemysław Morawiak, Wiktor Piecek, Przemysław Kula, Barbara Piętka, Dmitry D. Solnyshkov, G. Malpuech, Jacek Szczytko

Published Oct 16, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1126/sciadv.aee4875

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The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.

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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.
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.
Despite ground-breaking observations of supersolidity in spin-orbit-coupled Bose-Einstein condensates, until now the dynamics of the emerging spatially periodic density modulations has been vastly unexplored. Here, we demonstrate the nonrigidity of the density stripes in such a supersolid condensate and explore their dynamic behavior subject to spin perturbations. We show both analytically in infinite systems and numerically in the presence of a harmonic trap how spin waves affect the supersolid's density profile in the form of crystal waves, inducing oscillations of the periodicity as well as the orientation of the fringes. Both these features are well within reach of present-day experiments. Our results show that this system is a paradigmatic supersolid, featuring superfluidity in conjunction with a fully dynamic crystalline structure.
Spin-orbit-coupled Bose-Einstein condensates are a flexible experimental platform to engineer synthetic quantum many-body systems. In particular, they host the so-called stripe phase, an instance of a supersolid state of matter. The peculiar excitation spectrum of the stripe phase, a definite footprint of its supersolidity, has been difficult to measure experimentally. In this work, we performed in situ imaging of the stripes and directly observed both superfluid and crystal excitations. We investigated superfluid hydrodynamics and revealed a stripe compression mode, thus demonstrating that the system possesses a compressible crystalline structure. Through the frequency softening of this mode, we located the supersolid transition point. Our results establish spin-orbit-coupled supersolids as ideal systems to investigate supersolidity and its rich dynamics.
Exciton-polaritons, mixed light-matter quasiparticles in semiconductors, have recently shown evidence for Bose-Einstein condensation. Some of the properties of condensates of exciton-polaritons are reviewed in this article. We first discuss the spontaneous appearance of long-range order and the way this can be easily accessed in the case of polariton fluids. We show that the Penrose-Onsager criterion is valid even for such a very special case of condensate. We then describe the experiments that allow observation of topological defects in the fluid: quantized vortices, half vortices, and hyperbolic spin vortices. We demonstrate through the comparison with the gross Pitaevskii equation that the appearance and stability of such vortices are linked with the dissipative nature of the condensate together with the presence of disorder. We then briefly summarize the experiments on superfluid behavior of the polaritons at large-enough densities and expand somewhat more on the dynamical behavior of turbulence in the wake of an obstacle, with the appearance of vortex streets. We finally show that the Bogoliubov transformation has been revealed through four-wave mixing experiments.
The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this review we explore the properties of a spin-orbit-coupled Bose-Einstein condensate with equal Rashba and Dresselhaus strengths. This system presents a rich phase diagram, which exhibits a tricritical point separating a zero-momentum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.
The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.