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arXiv:2001.02584 · Physical Review A

Bardeen-Cooper-Schrieffer–type pairing in a spin- 12 Bose gas with spin-orbit coupling

M. Iskin

Published Jan 8, 2020• 0 citations
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Abstract

We apply the functional path-integral approach to analyze how the presence of a spin-orbit coupling (SOC) affects the basic properties of a BCS-type paired state in a two-component Bose gas. In addition to a mean-field theory that is based on the saddle-point approximation for the intercomponent pairing, we derive a Ginzburg-Landau theory by including the Gaussian fluctuations on top, and use them to reveal the crucial roles played by the momentum-space structure of an arbitrary SOC field in the stability of the paired state at finite temperatures. For this purpose, we calculate the critical transition temperature for the formation of paired bosons, and that of the gapless quasiparticle excitations for a broad range of interaction and SOC strengths. In support of our results for the many-body problem, we also benchmark our numerical calculations against the analytically tractable limits, and provide a full account of the two-body limit including its nonvanishing binding energy for arbitrarily weak interactions and the anisotropic effective mass tensor.

DOI
10.1103/physreva.101.013604

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We apply the functional path-integral approach to analyze how the presence of a spin-orbit coupling (SOC) affects the basic properties of a BCS-type paired state in a two-component Bose gas. In addition to a mean-field theory that is based on the saddle-point approximation for the intercomponent pairing, we derive a Ginzburg-Landau theory by including the Gaussian fluctuations on top, and use them to reveal the crucial roles played by the momentum-space structure of an arbitrary SOC field in the stability of the paired state at finite temperatures. For this purpose, we calculate the critical transition temperature for the formation of paired bosons, and that of the gapless quasiparticle excitations for a broad range of interaction and SOC strengths. In support of our results for the many-body problem, we also benchmark our numerical calculations against the analytically tractable limits, and provide a full account of the two-body limit including its nonvanishing binding energy for arbitrarily weak interactions and the anisotropic effective mass tensor.
We study the Bardeen–Cooper–Shrieffer (BCS) pairing state of a two-component Bose gas with a symmetric spin–orbit coupling (SOC). In the dilute limit at low temperature, this system is essentially a dilute gas of diatomic molecules. We compute the effective mass of the molecule and find that it is anisotropic in momentum space. The critical temperature of the pairing state is about eight times smaller than the Bose–Einstein condensation (BEC) transition temperature of an ideal Bose gas with the same density.
We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen–Cooper–Schrieffer (BCS) superconducting phase to a Bose–Einstein condensate (BEC), also in the presence of a spin–orbit coupling. Below a critical temperature the system is characterized by an order parameter. Generally a mean field approximation cannot reproduce the correct behavior of the critical temperature Tc over the whole crossover. We analyze the crucial role of quantum fluctuations beyond the mean-field approach useful to find Tc along the crossover in the presence of a spin–orbit coupling, within a path integral approach. A formal and detailed derivation for the set of equations useful to derive Tc is performed in the presence of Rashba, Dresselhaus and Zeeman couplings. In particular in the case of only Rashba coupling, for which the spin–orbit effects are more relevant, the two-body bound state exists for any value of the interaction, namely in the full crossover. As a result the effective masses of the emerging bosonic excitations are finite also in the BCS regime.
We study a two-component Bose gas with a symmetric spin-orbit coupling, and find that two atoms can form a bound state with any intra- or inter-species scattering length. Consequently, in the dilute limit, the Bardeen-Cooper-Shrieffer (BCS) pairing state of bosons can be formed with weakly-attractive inter-species and repulsive intra-species interactions. The quasiparticle excitation energies are anisotropic due to spin-orbit coupling. This BCS paring state is energetically favored over Bose-Einstein condensation (BEC) of atoms at low densities. As the density increases, there is a first-order transition from the BCS to BEC states.
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We consider a general anisotropic spin-orbit coupling and analyze the phase diagrams of both balanced and imbalanced Fermi gases for the entire BCS-BEC evolution. In the first part, we use the self-consistent mean-field theory at zero temperature, and show that the topological structure of the ground-state phase diagrams is quite robust against the effects of anisotropy. In the second part, we go beyond the mean-field description, and investigate the effects of Gaussian fluctuations near the critical temperature. This allows us to derive the time-dependent Ginzburg-Landau theory, from which we extract the effective mass of the Cooper pairs and their critical condensation temperature in the molecular BEC limit.
We study a two-component Bose gas with a symmetric spin-orbit coupling, and find that two atoms can form a bound state with any intra- or inter-species scattering length. Consequently, in the dilute limit, the BCS-pairing state of bosons can be formed with weakly attractive interspecies and repulsive intraspecies interactions. The quasiparticle excitation energies are anisotropic due to spin-orbit coupling. This BCS-pairing state is energetically favored over Bose-Einstein condensation (BEC) of atoms at low densities. As the density increases, there is a first-order transition from the BCS to BEC states.