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Physical Review A

Long-range superfluid order in trapped Bose-Einstein condensates with spin-orbit coupling

Gang Chen, Jie Ma, Suotang Jia

Published Oct 4, 2012• 4 citations
Publisher

Abstract

In this paper we explore the low-dimension long-range superfluid order in the trapped Bose-Einstein condensate driven by spin-orbit coupling at any finite temperature. With the help of the Bogoliubov inequality we give rigorous proofs in both one and two dimensions. For one dimension, no long-range superfluid order can be found, even if spin-orbit coupling exists. For two dimensions, we find that the long-range superfluid order cannot be ruled out in the presence of the unequal Rashba-Dresselhaus-type spin-orbit coupling. However, this long-range superfluid order disappears for the equal case, which has been achieved in recent experiments.

DOI
10.1103/physreva.86.045601

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In this paper we explore the low-dimension long-range superfluid order in the trapped Bose-Einstein condensate driven by spin-orbit coupling at any finite temperature. With the help of the Bogoliubov inequality we give rigorous proofs in both one and two dimensions. For one dimension, no long-range superfluid order can be found, even if spin-orbit coupling exists. For two dimensions, we find that the long-range superfluid order cannot be ruled out in the presence of the unequal Rashba-Dresselhaus-type spin-orbit coupling. However, this long-range superfluid order disappears for the equal case, which has been achieved in recent experiments.
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.
We study a two-dimensional spin-12\frac{1}{2}21​ interacting Bose-Einstein condensate with a Rashba-Dresselhaus spin-orbit coupling. The analytical expression of the superfluid density is derived from the linear response theory and Bogoliubov approximation. We find that the superfluid density can be divided into three terms, which originate from the condensate, the interaction between the condensate and the Bogoliubov excitations, and only the excitations. We show that the condensate-excitation interaction changes the bare mass in the superfluid density into the effective mass. In the isotropic spin-orbit coupling limit, the effective mass diverges, and the superfluid density is predicted to be zero within previous studies; however, our work shows that the excitation-induced superfluid density remains nonzero, which means that quantum fluctuations rescue the superfluidity. Our results show the importance of the quantum fluctuations in understanding the superfluid properties of spin-orbit-coupled Bose-Einstein condensates.
We discuss the evolution from BCS to Bose-Einstein condensate (BEC) superfluids in the presence of spin-orbit coupling for a balanced mixture of ultracold fermions. The dependence of several thermodynamic properties, such as chemical potential, order parameter, pressure, entropy, isothermal compressibility, and spin susceptibility tensor on the spin-orbit coupling and interaction parameter at low temperatures are analyzed. We studied both equal Rashba and Dresselhaus (ERD) and the Rashba-only (RO) spin-orbit coupling. Comparisons between the two cases reveal several striking differences in the corresponding thermodynamic quantities. Finally, we propose measuring the isothermal compressibility and spin susceptibility as a way of detecting the effects of the spin-orbit coupling.
A finite-size quasi-two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and the balanced, effectively one-dimensional Rashba-Dresselhaus one. In both cases spin-dependent ``anomalous'' velocity, proportional to the spin-orbit-coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wave packets, reducing the total condensate density. Depending on the spin-orbit-coupling strength, interatomic attraction, and initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus extending the domain of existence of condensates of attracting atoms.
We obtain the superfluid transition temperature of equal Rashba-Dresselhaus spin-orbit and Rabi coupled Fermi superfluids, from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) regimes in three dimensions. Spin-orbit coupling enhances the critical temperature in the BEC limit, and can convert a first order phase transition in the presence of Rabi coupling into second order, as a function of the Rabi coupling for fixed interactions. We derive the Ginzburg-Landau equation to sixth power in the superfluid order parameter to describe both first and second order transitions as a function of spin-orbit and Rabi couplings.