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arXiv:2410.06318 · Physical Review A

Spin-orbit-coupled mean-field Bose gas at finite temperature

Paweł Jakubczyk, Marek Napiórkowski

Published Nov 7, 2024• 2 citations
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Abstract

We consider the spin-orbit-coupled Bose gas with repulsive mean-field interparticle interactions. We analyze the phase diagram of the system varying the temperature $T>0$, the chemical potentials, and interparticle and spin-orbit interaction couplings. Our results indicate that, for Rashba- and Weyl-type spin-orbit couplings, condensates featuring an ordering wave vector $\stackrel{P\vec}{Q}\ensuremath{\ne}\stackrel{P\vec}{0}$ are fragile with respect to thermal fluctuations and at $T>0$ the only stable thermodynamic phases involving the Bose-Einstein condensate (BEC) are those of uniform type with $\stackrel{P\vec}{Q}=\stackrel{P\vec}{0}$. On the other hand, the presence of the spin-orbit coupling stabilizes the $\stackrel{P\vec}{Q}=\stackrel{P\vec}{0}$ BEC state at any dimensionality $d>1$ and modifies either the order or the universality class of the corresponding phase transition. We emphasize the singular nature of the limit of vanishing spin-orbit interaction coupling $v$, sizable shifts of the phase boundaries upon varying $v$, and the role of the relative magnitudes of the interparticle interaction couplings for the character of the condensation transition.

DOI
10.1103/physreva.110.053304

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We consider the spin-orbit-coupled Bose gas with repulsive mean-field interparticle interactions. We analyze the phase diagram of the system varying the temperature T>0T>0T>0, the chemical potentials, and interparticle and spin-orbit interaction couplings. Our results indicate that, for Rashba- and Weyl-type spin-orbit couplings, condensates featuring an ordering wave vector \stackrel{P\vec}{Q}\ensuremath{\ne}\stackrel{P\vec}{0} are fragile with respect to thermal fluctuations and at T>0T>0T>0 the only stable thermodynamic phases involving the Bose-Einstein condensate (BEC) are those of uniform type with \stackrel{P\vec}{Q}=\stackrel{P\vec}{0}. On the other hand, the presence of the spin-orbit coupling stabilizes the \stackrel{P\vec}{Q}=\stackrel{P\vec}{0} BEC state at any dimensionality d>1d>1d>1 and modifies either the order or the universality class of the corresponding phase transition. We emphasize the singular nature of the limit of vanishing spin-orbit interaction coupling vvv, sizable shifts of the phase boundaries upon varying vvv, and the role of the relative magnitudes of the interparticle interaction couplings for the character of the condensation transition.
We study the stability of Bose condensates with Rashba-Dresselhaus spin-orbit coupling in three dimensions against quantum and thermal fluctuations. The ground state depletion of the plane-wave condensate due to quantum fluctuations is, as we show, finite, and therefore the condensate is stable. We also calculate the corresponding shift of the ground state energy. Although the system cannot condense in the absence of interparticle interactions, by estimating the number of excited particles we show that interactions stabilize the condensate even at nonzero temperature. Unlike in the usual Bose gas, the normal phase is not kinematically forbidden at any temperature; calculating the free energy of the normal phase at finite temperature, and comparing with the free energy of the condensed state, we infer that generally the system is condensed at zero temperature, and undergoes a transition to normal at nonzero temperature.
Cold atomic Bose-Einstein systems in the presence of simulated Rashba- Dresselhaus spin-orbit coupling exhibit novel physical features. With pure in-plane Rashba coupling the system is predicted in Bogoliubov-Hartree-Fock to have a stable Bose condensate below a critical temperature, even though the effective density of states is two-dimensional. In addition the system has a normal state at all temperatures. We review here the new physics when the system has such spin-orbit coupling, and discuss the nature of the finite temperature condensation phase transition from the normal to condensed phases.
A Bose gas subject to a light-induced Rashba spin-orbit coupling possesses a dispersion minimum on a circle in momentum space; we show that kinematic constraints due to this dispersion cause interactions to renormalize to universal, angle-dependent values that govern the phase structure in the dilute-gas limit. We find that, regardless of microscopic interactions, (a) the ground state involves condensation at two opposite momenta and is, in finite systems, a fragmented condensate and and (b) there is a nonzero-temperature instability toward the condensation of pairs of bosons. We discuss how our results can be reconciled with the qualitatively different mean-field phase diagram, which is appropriate for dense gases.
We consider a spin-orbit coupled configuration of spin-1/2 interacting bosons with equal Rashba and Dresselhaus couplings. The phase diagram of the system at T=0 is discussed with special emphasis on the role of the interaction treated in the mean-field approximation. For a critical value of the density and of the Raman coupling we predict the occurrence of a characteristic tricritical point separating the spin mixed, the phase separated, and the zero momentum states of the Bose gas. The corresponding quantum phases are investigated analyzing the momentum distribution, the longitudinal and transverse spin polarization, and the emergence of density fringes. The effect of harmonic trapping as well as the role of the breaking of spin symmetry in the interaction Hamiltonian are also discussed.
We determine the finite-temperature phase diagram of two-dimensional bosons with two hyperfine (pseudospin) states coupled via a Rashba-Dresselhaus spin-orbit interaction using classical field Monte Carlo calculations. For anisotropic spin-orbit coupling, we find a transition to a Berezinskii-Kosterlitz-Thouless superfluid phase with quasi-long-range order. We show that the spin order of the quasicondensate is driven by the anisotropy of the interparticle interaction, favoring either a homogeneous plane-wave state or stripe phase with broken translational symmetry. Both phases show characteristic behavior in the algebraically decaying spin-density correlation function. For a fully isotropic interparticle interaction, our calculations indicate a fractionalized quasicondensate where the mean-field degeneracy of the plane-wave and stripe phase remains robust against critical fluctuations. In the case of fully isotropic spin-orbit coupling, the circular degeneracy of the single-particle ground state destroys the algebraic ordered phase in the thermodynamic limit, but a crossover remains for finite-size systems.
Abstract We revisit the structure of the phase diagram of the two-component mean-field Bose mixture at finite temperatures, considering both the cases of attractive and repulsive interspecies interactions. In particular, we analyze the evolution of the phase diagram upon driving the system towards collapse and point out its distinctive features in this limit. We provide analytical insights into the global structure of the phase diagram and the properties of the phase transitions between the normal phase and the phases involving Bose–Einstein condensates. Inter alia we analytically demonstrate that for sufficiently weak interspecies interactions a 12 the system generically exhibits a line of quadruple points but has no triple nor tricritical points in the phase diagram spanned by the chemical potentials µ 1, µ 2 and temperature T. In contrast, for sufficiently large, positive values of a 12, the system displays both triple and tricritical points but no quadruple points. As pointed out in recent studies, in addition to the phase transitions involving condensation, the mixture may be driven through a liquid–gas type transition, and we clarify the conditions for its occurrence. We finally discuss the impact of interaction- and mass-imbalance on the phase diagram of the mixture.