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arXiv:2506.08830

Cavity-Mediated Gas-Liquid Transition

Fan Zhang, Haowei Li, Yi Wei

Published Jun 10, 2025• 0 citations
arXivHTMLPDF

Abstract

We study the gas-liquid transition in a binary Bose-Einstein condensate, where the two Zeeman-shifted hyperfine spin components are coupled by cavity-assisted Raman processes. Below a critical Zeeman field, the cavity becomes superradiant for an infinitesimally small pumping strength, where the enhanced superradiance is facilitated by the simultaneous formation of quantum droplet, a self-bound liquid phase stabilized by quantum fluctuations. Above the critical Zeeman field, the gas-liquid transition only takes place at a finite pumping strength after the system becomes superradiant. As the back action of the gas-liquid transition, the superradiant cavity field undergoes an abrupt jump at the first-order transition point. Furthermore, as a result of the fixed density ratio of the quantum droplet, the cavity field exhibits a linear scaling with the pumping strength in the liquid phase. These features serve as prominent signals for the cavity-mediated gas-liquid transition and coexistence, which derive from the interplay of Zeeman field, cavity-assisted spin mixing, and quantum fluctuations.

DOI
10.48550/arxiv.2506.08830

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We study the gas-liquid transition in a binary Bose-Einstein condensate, where the two Zeeman-shifted hyperfine spin components are coupled by cavity-assisted Raman processes. Below a critical Zeeman field, the cavity becomes superradiant for an infinitesimally small pumping strength, where the enhanced superradiance is facilitated by the simultaneous formation of quantum droplet, a self-bound liquid phase stabilized by quantum fluctuations. Above the critical Zeeman field, the gas-liquid transition only takes place at a finite pumping strength after the system becomes superradiant. As the back action of the gas-liquid transition, the superradiant cavity field undergoes an abrupt jump at the first-order transition point. Furthermore, as a result of the fixed density ratio of the quantum droplet, the cavity field exhibits a linear scaling with the pumping strength in the liquid phase. These features serve as prominent signals for the cavity-mediated gas-liquid transition and coexistence, which derive from the interplay of Zeeman field, cavity-assisted spin mixing, and quantum fluctuations.
Quantum liquid, in the form of a self-bound droplet, is stabilized by a subtle balance between the mean-field contribution and quantum fluctuations. While a liquid-gas transition is expected when such a balance is broken, it remains elusive whether liquid-gas critical points exist in the quantum regime. Here, we study the quantum criticality in a binary Bose mixture undergoing the liquid-gas transition. We show that, beyond a narrow stability window of the self-bound liquid, a liquid-gas coexistence persists, which eventually transits into a homogeneous mixture. Importantly, we identify two distinct critical points where the liquid-gas coexistence terminates. These critical points are characterized by rich critical behaviors in their vicinity, including divergent susceptibility, unique phonon-mode softening, and enhanced density correlations. The liquid-gas transition and the critical points can be readily explored in ultracold atoms confined to a box potential. Our work highlights the thermodynamic approach as a powerful tool in revealing the quantum liquid-gas criticality, and paves the way for further studies of critical phenomena in quantum liquids.
We explore the many-body phases of a two-dimensional Bose-Einstein condensate with cavity-mediated dynamic spin-orbit coupling. With the help of two transverse noninterfering, counterpropagating pump lasers and a single standing-wave cavity mode, two degenerate Zeeman sub-levels of the quantum gas are Raman coupled in a double-$\mathrm{\ensuremath{\Lambda}}$-configuration. Beyond a critical pump strength the cavity mode is populated via coherent superradiant Raman scattering from the two pump lasers, leading to the appearance of a dynamical spin-orbit coupling for the atoms. We identify three quantum phases with distinct atomic and photonic properties: the normal ``homogeneous'' phase, the superradiant ``spin-helix'' phase, and the superradiant ``supersolid spin-density-wave'' phase. The last exhibits an emergent periodic atomic density distribution with an orthorhombic centered rectangular-lattice structure due to the interplay between the coherent photon scattering into the resonator and the collision-induced momentum coupling. The transverse lattice spacing of the emergent crystal is set by the dynamic spin-orbit coupling.
We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z_{2} symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative phase of the two condensate wave functions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially averaged relative condensate phase is locked at either π/2 or -π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.
We observe the joint spin-spatial (spinor) self-organization of a two-component Bose-Einstein condensate (BEC) strongly coupled to an optical cavity. This unusual nonequilibrium Hepp-Lieb-Dicke phase transition is driven by an off-resonant Raman transition formed from a classical pump field and the emergent quantum dynamical cavity field. This mediates a spinor-spinor interaction that, above a critical strength, simultaneously organizes opposite spinor states of the BEC on opposite checkerboard configurations of an emergent 2D lattice. The resulting spinor density-wave polariton condensate is observed by directly detecting the atomic spin and momentum state and by holographically reconstructing the phase of the emitted cavity field. The latter provides a direct measure of the spin state, and a spin-spatial domain wall is observed. The photon-mediated spin interactions demonstrated here may be engineered to create dynamical gauge fields and quantum spin glasses.
Quantum droplets are formed in quantum many-body systems when the competition of quantum corrections with the mean-field interaction yields a stable self-bound quantum liquid. We predict the emergence of a quantum droplet when a Bose-Einstein condensate is placed in a transverse-pumped optical cavity. The strong coupling between the atoms and a cavity mode induces long-range interactions in the atoms, and a roton mode for negative cavity detuning emerges. Using Bogoliubov theory, we show that the roton mode competes with the repulsive atomic s -wave scattering. Due to the favorable scaling of the quantum fluctuations with respect to the volume, a self-bound stable quantum liquid emerges.
We realize the dynamical 1D spin-orbit coupling (SOC) of a Bose-Einstein condensate confined within an optical cavity. The SOC emerges through spin-correlated momentum impulses delivered to the atoms via Raman transitions. These are effected by classical pump fields acting in concert with the quantum dynamical cavity field. Above a critical pump power, the Raman coupling emerges as the atoms superradiantly populate the cavity mode with photons. Concomitantly, these photons cause a backaction onto the atoms, forcing them to order their spin-spatial state. This SOC-inducing superradiant Dicke phase transition results in a spinor-helix polariton condensate. We observe emergent SOC through spin-resolved atomic momentum imaging and temporal heterodyne measurement of the cavity-field emission. Dynamical SOC in quantum gas cavity QED, and the extension to dynamical gauge fields, may enable the creation of Meissner-like effects, topological superfluids, and exotic quantum Hall states in coupled light-matter systems.