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:1706.06234 · Physical Review A

Symmetry-enriched Bose-Einstein condensates in a spin-orbit-coupled bilayer system

Jia-Ming Cheng, Xiang-Fa Zhou, Zheng-Wei Zhou, Guang‐Can Guo, Ming Gong

Published Jan 22, 2018• 4 citations
arXivHTMLPDF

Abstract

We consider the fate of Bose-Einstein condensation with time-reversal symmetry and inversion symmetry in a spin-orbit-coupled bilayer system. When these two symmetry operators commute, all the single-particle bands are exactly twofold degenerate in the momentum space. The scattering in the twofold-degenerate rings can relax the spin-momentum locking effect from spin-orbit-coupling interaction and thus can realize the spin-polarized plane-wave phase even when the interparticle interaction dominates. When these two operators anticommute, the lowest two bands may have the same minimal energy, but with totally different spin structures. As a result, the competition between different condensates in these two energetically degenerate rings can give rise to different stripe phases with atoms condensed at two or four collinear momenta. We find that the crossover between these two cases is accompanied by the excited band condensation when the interference energy can overcome the increased single-particle energy in the excited band. This effect is not based on strong interaction and thus can be realized even with moderate interaction strength.

DOI
10.1103/physreva.97.013625

Related papers

Tunneling-assisted spin-orbit coupling in bilayer Bose-Einstein condensates

Qing Sun, Lin Wen, W.M. Liu +2 more

Motivated by the goal of realizing spin-orbit coupling (SOC) beyond one dimension, we propose and analyze a method to generate effective two-dimensional SOC in bilayer BECs with laser-assisted interlayer tunneling. We show that interplay among the interlayer tunneling, SOC, and intralayer atomic interaction can give rise to diverse ground-state configurations. In particular, the system undergoes a transition to a different type of stripe phase which spontaneously breaks the time-reversal symmetry. Different from the ordinary Rashba-type SOC, a fractionalized skyrmion lattice emerges spontaneously in the bilayer system without external traps. Furthermore, we predict the occurrence of a tetracritical point in the phase diagram of the bilayer BECs, where four phases merge. The origin of the different emerging phases is elucidated.

arXiv:1403.4338•Physical Review A•Mar 16, 2015•26 citations

Time-reversal-invariant spin-orbit-coupled bilayer Bose-Einstein condensates

Matthew Maisberger, Lincheng Wang, Kuei Sun +2 more

Time-reversal invariance plays a crucial role for many exotic quantum phases, particularly for topologically nontrivial states, in spin-orbit coupled electronic systems. Recently realized spin-orbit coupled cold-atom systems, however, lack the time-reversal symmetry due to the inevitable presence of an effective transverse Zeeman field. We address this issue by analyzing a realistic scheme to preserve time-reversal symmetry in spin-orbit-coupled ultracold atoms, with the use of Hermite-Gaussian-laser-induced Raman transitions that preserve spin-layer time-reversal symmetry. We find that the system's quantum states form Kramers pairs, resulting in symmetry-protected gap closing of the lowest two bands at arbitrarily large Raman coupling. We also show that Bose gases in this setup exhibit interaction-induced layer-stripe and uniform phases as well as intriguing spin-layer symmetry and spin-layer correlation.

arXiv:1710.08323•Physical Review A•May 29, 2018•2 citations

Traveling supersolid stripe patterns in spin-orbit-coupled Bose-Einstein condensates

Giovanni Italo Martone, Georgy V. Shlyapnikov

We consider a traveling supersolid stripe pattern in a spin-orbit-coupled Bose gas. This configuration is associated with an unequal population of the two single-particle energy minima, giving rise to a chemical potential difference that sets the fringe velocity. Unlike stationary stripes, the moving pattern is spin-polarized, with decreasing contrast as the population imbalance increases, eventually leading to stripe melting and transition to the uniform plane-wave phase. The Bogoliubov spectrum of the moving stripes exhibits asymmetry under inversion of the excitation quasimomentum. At high population imbalance, we identify energetic and dynamical instabilities in the spin-phonon mode which transforms to the roton mode of the plane-wave phase as the stripe structure vanishes.

arXiv:2506.07322•Physical Review A•Jan 14, 2026•1 citation

Spin-Orbit Coupled Spinor Bose-Einstein Condensates

Chunji Wang, Chao Gao, Chao‐Ming Jian +1 more

An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.

arXiv:1006.5148•Physical Review Letters•Oct 13, 2010•645 citations

Enhanced stripe phases in spin-orbit-coupled Bose-Einstein condensates in ring cavities

Farokh Mivehvar, David L. Feder

The coupled dynamics of the atom and photon fields in optical ring cavities with two counterpropagating modes give rise to both spin-orbit interactions as well as long-ranged interactions between atoms of a many-body system. At zero temperature, the interplay between the two-body and cavity-mediated interactions determines the ground state of a Bose-Einstein condensate. In this work, we find that cavity quantum electrodynamics in the weak-coupling regime favors a stripe-phase state over a plane-wave phase as the strength of cavity-mediated interactions increases. Indeed, the stripe phase is energetically stabilized even for condensates with attractive intraspecies and interspecies interactions for sufficiently large cavity interactions. The elementary excitation spectra in both phases correspond to linear dispersion relation at long wavelengths, indicating that both phases exhibit superfluidity, although the plane-wave phase also displays a characteristic roton-type feature. The results suggest that even in the weak-coupling regime, cavities can yield interesting new physics in ultracold quantum gases.

arXiv:1505.02189•Physical Review A•Aug 10, 2015•27 citations

SPIN-ORBIT-COUPLED BOSE-EINSTEIN CONDENSATES

Yun Li, Giovanni Italo Martone, S. Stringari

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.

arXiv:1410.5526•Annual review of cold atoms and molecules•Mar 24, 2015•42 citations
We consider the fate of Bose-Einstein condensation with time-reversal symmetry and inversion symmetry in a spin-orbit-coupled bilayer system. When these two symmetry operators commute, all the single-particle bands are exactly twofold degenerate in the momentum space. The scattering in the twofold-degenerate rings can relax the spin-momentum locking effect from spin-orbit-coupling interaction and thus can realize the spin-polarized plane-wave phase even when the interparticle interaction dominates. When these two operators anticommute, the lowest two bands may have the same minimal energy, but with totally different spin structures. As a result, the competition between different condensates in these two energetically degenerate rings can give rise to different stripe phases with atoms condensed at two or four collinear momenta. We find that the crossover between these two cases is accompanied by the excited band condensation when the interference energy can overcome the increased single-particle energy in the excited band. This effect is not based on strong interaction and thus can be realized even with moderate interaction strength.
Motivated by the goal of realizing spin-orbit coupling (SOC) beyond one dimension, we propose and analyze a method to generate effective two-dimensional SOC in bilayer BECs with laser-assisted interlayer tunneling. We show that interplay among the interlayer tunneling, SOC, and intralayer atomic interaction can give rise to diverse ground-state configurations. In particular, the system undergoes a transition to a different type of stripe phase which spontaneously breaks the time-reversal symmetry. Different from the ordinary Rashba-type SOC, a fractionalized skyrmion lattice emerges spontaneously in the bilayer system without external traps. Furthermore, we predict the occurrence of a tetracritical point in the phase diagram of the bilayer BECs, where four phases merge. The origin of the different emerging phases is elucidated.
Time-reversal invariance plays a crucial role for many exotic quantum phases, particularly for topologically nontrivial states, in spin-orbit coupled electronic systems. Recently realized spin-orbit coupled cold-atom systems, however, lack the time-reversal symmetry due to the inevitable presence of an effective transverse Zeeman field. We address this issue by analyzing a realistic scheme to preserve time-reversal symmetry in spin-orbit-coupled ultracold atoms, with the use of Hermite-Gaussian-laser-induced Raman transitions that preserve spin-layer time-reversal symmetry. We find that the system's quantum states form Kramers pairs, resulting in symmetry-protected gap closing of the lowest two bands at arbitrarily large Raman coupling. We also show that Bose gases in this setup exhibit interaction-induced layer-stripe and uniform phases as well as intriguing spin-layer symmetry and spin-layer correlation.
We consider a traveling supersolid stripe pattern in a spin-orbit-coupled Bose gas. This configuration is associated with an unequal population of the two single-particle energy minima, giving rise to a chemical potential difference that sets the fringe velocity. Unlike stationary stripes, the moving pattern is spin-polarized, with decreasing contrast as the population imbalance increases, eventually leading to stripe melting and transition to the uniform plane-wave phase. The Bogoliubov spectrum of the moving stripes exhibits asymmetry under inversion of the excitation quasimomentum. At high population imbalance, we identify energetic and dynamical instabilities in the spin-phonon mode which transforms to the roton mode of the plane-wave phase as the stripe structure vanishes.
An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.
The coupled dynamics of the atom and photon fields in optical ring cavities with two counterpropagating modes give rise to both spin-orbit interactions as well as long-ranged interactions between atoms of a many-body system. At zero temperature, the interplay between the two-body and cavity-mediated interactions determines the ground state of a Bose-Einstein condensate. In this work, we find that cavity quantum electrodynamics in the weak-coupling regime favors a stripe-phase state over a plane-wave phase as the strength of cavity-mediated interactions increases. Indeed, the stripe phase is energetically stabilized even for condensates with attractive intraspecies and interspecies interactions for sufficiently large cavity interactions. The elementary excitation spectra in both phases correspond to linear dispersion relation at long wavelengths, indicating that both phases exhibit superfluidity, although the plane-wave phase also displays a characteristic roton-type feature. The results suggest that even in the weak-coupling regime, cavities can yield interesting new physics in ultracold quantum gases.
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.