Bardeen-Cooper-Schrieffer--type pairing in a spin-$\frac{1}{2}$ Bose gas with spin-orbit coupling

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 inter-component 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 non-vanishing binding energy for arbitrarily weak interactions and the anisotropic effective mass tensor.

arXiv comment6 pages with 2 figures; to appear in PRA

References in corpus (16)

• Theory of ultracold Fermi gases
• Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
• Atom--Molecule Coherence in a Bose-Einstein Condensate
• Experimental realization of a two-dimensional synthetic spin-orbit coupling in ultracold Fermi gases
• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• Formation of Quantum-Degenerate Sodium Molecules
• Experimental observation of a topological band gap opening in ultracold Fermi gases with two-dimensional spin-orbit coupling
• Ultracold Molecule Production Via a Resonant Oscillating Magnetic Field
• Superfluid transitions in bosonic atom-molecule mixtures near Feshbach resonance
• High Controllable and Robust 2D Spin-Orbit Coupling for Quantum Gases
• Quantum phases of atomic Fermi gases with anisotropic spin-orbit coupling
• A strongly interacting Bose gas: Nozières and Schmitt-Rink theory and beyond
• Pairing Instability and Mechanical Collapse of a Bose Gas with an Attractive Interaction
• Molecular Bose-Einstein condensation in a Bose gas with a wide Feshbach resonance at finite temperatures
• BCS pairing state of a Dilute Bose Gas with Spin-Orbit Coupling
• Rashbon condensation in a Bose gas with Rashba spin-orbit coupling