Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1801.00756 · Physical Review Letters

Driven-Dissipative Supersolid in a Ring Cavity

Farokh Mivehvar, Stefan Ostermann, Francesco Piazza, Helmut Ritsch

Published Mar 23, 2018• 57 citations
arXivHTMLPDF

Abstract

Supersolids are characterized by the counterintuitive coexistence of superfluid and crystalline order. Here we study a supersolid phase emerging in the steady state of a driven-dissipative system. We consider a transversely pumped Bose-Einstein condensate trapped along the axis of a ring cavity and coherently coupled to a pair of degenerate counterpropagating cavity modes. Above a threshold pump strength the interference of photons scattered into the two cavity modes results in an emergent superradiant lattice, which spontaneously breaks the continuous translational symmetry towards a periodic atomic pattern. The crystalline steady state inherits the superfluidity of the Bose-Einstein condensate, thus exhibiting genuine properties of a supersolid. A gapless collective Goldstone mode correspondingly appears in the superradiant phase, which can be nondestructively monitored via the relative phase of the two cavity modes on the cavity output. Despite cavity-photon losses the Goldstone mode remains undamped, indicating the robustness of the supersolid phase.

DOI
10.1103/physrevlett.120.123601

Related papers

Self-ordered supersolid phase beyond Dicke superradiance in a ring cavity

Yuangang Deng, Su Yi

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.

arXiv:2201.07664•Physical Review Research•Jan 3, 2023•9 citations

Supersolid Properties of a Bose-Einstein Condensate in a Ring Resonator

S. Schuster, P. Wolf, Stefan Ostermann +2 more

We investigate the dynamics of a Bose-Einstein condensate interacting with two noninterfering and counterpropagating modes of a ring resonator. Superfluid, supersolid, and dynamic phases are identified experimentally and theoretically. The supersolid phase is obtained for sufficiently equal pump strengths for the two modes. In this regime we observe the emergence of a steady state with crystalline order, which spontaneously breaks the continuous translational symmetry of the system. The supersolidity of this state is demonstrated by the conservation of global phase coherence at the superfluid to supersolid phase transition. Above a critical pump asymmetry the system evolves into a dynamic runaway instability commonly known as collective atomic recoil lasing. We present a phase diagram and characterize the individual phases by comparing theoretical predictions with experimental observations.

arXiv:1908.10932•Physical Review Letters•Apr 6, 2020•56 citations

Z n symmetry broken supersolid in spin–orbit-coupled Bose–Einstein condensates

Ze-Hong Guo, Qizhong Zhu

Abstract Supersolid is an exotic state of matter characterized by both superfluid properties and periodic particle density modulation, due to spontaneous breaking of U(1) gauge symmetry and spatial translation symmetry, respectively. For conventional supersolids, continuous translation symmetry breaking is accompanied by one gapless Goldstone mode in the excitation spectra. An interesting question naturally arises: what is the consequence of breaking discrete translation symmetry for supersolids? In this work, we study the consequence of discrete symmetry breaking in a Z n supersolid resulting from spontaneous breaking of a discrete Z n symmetry, or equivalently, a discrete translation symmetry. This Z n supersolid is realized in the stripe phase of spin–orbit-coupled Bose–Einstein condensate under an external periodic potential with period 1 / n of intrinsic stripe period. For n ⩾ 2 , there are n degenerate ground states with spontaneously broken lattice translation symmetry. The low-energy excitations of Z n supersolid include a pseudo-Goldstone mode, whose excitation gap at long wavelength limit is found to decrease rapidly with n. We further numerically show that, when confined in a harmonic trap, a spin-dependent perturbation can result in the transition between degenerate ground states of Z n supersolid. With the integer n tunable using the experimental technique of generating subwavelength optical lattice, the Z n supersolid proposed here offers a cold atom platform to simulate physics related with generic Z n symmetry breaking in a highly controllable setting.

arXiv:2305.12069•New Journal of Physics•Nov 29, 2024•2 citations

Supersolid Rotation in an Annular Bose-Einstein Condensate coupled to a Ring Cavity

Gunjan Yadav, Nilamoni Daloi, Pardeep Kumar +2 more

We theoretically investigate an annularly confined Bose-Einstein Condensate (BEC) coupled to a four-mirror ring cavity supporting traveling-wave optical modes. Under symmetric driving by counter-propagating Laguerre-Gaussian beams carrying equal and opposite orbital angular momenta, the system realizes supersolid phases coexisting with persistent superfluid circulation. Specifically, we obtain a supersolid state if we start with a BEC of winding number $L_p$ as well as supersolid packets with coherent superpositions of two different BEC $L_p$ values. Under asymmetric pumping, realized with Laguerre-Gaussian beams of different orbital angular momenta, chiral symmetry is broken in the system, resulting in asymmetric cavity field amplitudes, directional density modulations, and tunable rotational dynamics of the resulting supersolid lattice. This leads to rotating supersolid density structures for a single winding-number state, and rotating wave packets for an initial superposition of rotational eigenstates. Finally, we probe the presence of Goldstone and Higgs modes which can be observed using minimally destructive measurements of the cavity output spectrum. Our mean-field theory reveals interference-driven rotation without physical stirring, and distinguishes our work from prior static cavity supersolids. Our results establish the ring cavity annular BEC as a versatile platform for generating chiral quantum matter, implementing rotation-sensing devices and generating atomtronic circuits with supersolids.

cond-mat.quant-gasCross-listedarXiv:2604.16573•Physical Review A•Apr 20, 2026•0 citations

Supersolid gap soliton in a Bose-Einstein condensate and optical ring cavity coupling system

Jieli Qin, Lu Zhou

The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.

arXiv:2206.03706•Physical review. E•May 31, 2022•9 citations

Phase transition, phase separation and mode softening of a two-component Bose-Einstein condensate in an optical cavity

Jia-Ying Lin, Wei Qin, Renyuan Liao

We investigate the superradiant phase transition in a two-component Bose-Einstein condensate with distinct atomic detunings, confined in an optical cavity and driven by a transverse pump laser. By combining perturbation theory and numerical simulations, we demonstrate that the phase transition is dominated by the red-detuned component, resulting in a phase diagram completely different from that of a single-component case under blue-detuned condition. The system exhibits spontaneous phase separation between the two components, manifested as alternating stripe patterns in the normal phase and distinct Bragg gratings in the superradiant phase. Furthermore, the Bogoliubov excitation spectrum reveals roton-type mode softening, indicating that the phase transition also corresponds to the superfluid-to-lattice supersolid transition. Our findings provide insights into the interplay between atomic detunings and collective quantum many-body phenomena, offering potential applications in quantum simulation and optical switching technologies.

cond-mat.quant-gasCross-listedarXiv:2601.07772•Physical Review A•Jan 13, 2026•1 citation
Supersolids are characterized by the counterintuitive coexistence of superfluid and crystalline order. Here we study a supersolid phase emerging in the steady state of a driven-dissipative system. We consider a transversely pumped Bose-Einstein condensate trapped along the axis of a ring cavity and coherently coupled to a pair of degenerate counterpropagating cavity modes. Above a threshold pump strength the interference of photons scattered into the two cavity modes results in an emergent superradiant lattice, which spontaneously breaks the continuous translational symmetry towards a periodic atomic pattern. The crystalline steady state inherits the superfluidity of the Bose-Einstein condensate, thus exhibiting genuine properties of a supersolid. A gapless collective Goldstone mode correspondingly appears in the superradiant phase, which can be nondestructively monitored via the relative phase of the two cavity modes on the cavity output. Despite cavity-photon losses the Goldstone mode remains undamped, indicating the robustness of the supersolid phase.
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.
We investigate the dynamics of a Bose-Einstein condensate interacting with two noninterfering and counterpropagating modes of a ring resonator. Superfluid, supersolid, and dynamic phases are identified experimentally and theoretically. The supersolid phase is obtained for sufficiently equal pump strengths for the two modes. In this regime we observe the emergence of a steady state with crystalline order, which spontaneously breaks the continuous translational symmetry of the system. The supersolidity of this state is demonstrated by the conservation of global phase coherence at the superfluid to supersolid phase transition. Above a critical pump asymmetry the system evolves into a dynamic runaway instability commonly known as collective atomic recoil lasing. We present a phase diagram and characterize the individual phases by comparing theoretical predictions with experimental observations.
Abstract Supersolid is an exotic state of matter characterized by both superfluid properties and periodic particle density modulation, due to spontaneous breaking of U(1) gauge symmetry and spatial translation symmetry, respectively. For conventional supersolids, continuous translation symmetry breaking is accompanied by one gapless Goldstone mode in the excitation spectra. An interesting question naturally arises: what is the consequence of breaking discrete translation symmetry for supersolids? In this work, we study the consequence of discrete symmetry breaking in a Z n supersolid resulting from spontaneous breaking of a discrete Z n symmetry, or equivalently, a discrete translation symmetry. This Z n supersolid is realized in the stripe phase of spin–orbit-coupled Bose–Einstein condensate under an external periodic potential with period 1 / n of intrinsic stripe period. For n ⩾ 2 , there are n degenerate ground states with spontaneously broken lattice translation symmetry. The low-energy excitations of Z n supersolid include a pseudo-Goldstone mode, whose excitation gap at long wavelength limit is found to decrease rapidly with n. We further numerically show that, when confined in a harmonic trap, a spin-dependent perturbation can result in the transition between degenerate ground states of Z n supersolid. With the integer n tunable using the experimental technique of generating subwavelength optical lattice, the Z n supersolid proposed here offers a cold atom platform to simulate physics related with generic Z n symmetry breaking in a highly controllable setting.
We theoretically investigate an annularly confined Bose-Einstein Condensate (BEC) coupled to a four-mirror ring cavity supporting traveling-wave optical modes. Under symmetric driving by counter-propagating Laguerre-Gaussian beams carrying equal and opposite orbital angular momenta, the system realizes supersolid phases coexisting with persistent superfluid circulation. Specifically, we obtain a supersolid state if we start with a BEC of winding number LpL_pLp​ as well as supersolid packets with coherent superpositions of two different BEC LpL_pLp​ values. Under asymmetric pumping, realized with Laguerre-Gaussian beams of different orbital angular momenta, chiral symmetry is broken in the system, resulting in asymmetric cavity field amplitudes, directional density modulations, and tunable rotational dynamics of the resulting supersolid lattice. This leads to rotating supersolid density structures for a single winding-number state, and rotating wave packets for an initial superposition of rotational eigenstates. Finally, we probe the presence of Goldstone and Higgs modes which can be observed using minimally destructive measurements of the cavity output spectrum. Our mean-field theory reveals interference-driven rotation without physical stirring, and distinguishes our work from prior static cavity supersolids. Our results establish the ring cavity annular BEC as a versatile platform for generating chiral quantum matter, implementing rotation-sensing devices and generating atomtronic circuits with supersolids.
The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.
We investigate the superradiant phase transition in a two-component Bose-Einstein condensate with distinct atomic detunings, confined in an optical cavity and driven by a transverse pump laser. By combining perturbation theory and numerical simulations, we demonstrate that the phase transition is dominated by the red-detuned component, resulting in a phase diagram completely different from that of a single-component case under blue-detuned condition. The system exhibits spontaneous phase separation between the two components, manifested as alternating stripe patterns in the normal phase and distinct Bragg gratings in the superradiant phase. Furthermore, the Bogoliubov excitation spectrum reveals roton-type mode softening, indicating that the phase transition also corresponds to the superfluid-to-lattice supersolid transition. Our findings provide insights into the interplay between atomic detunings and collective quantum many-body phenomena, offering potential applications in quantum simulation and optical switching technologies.