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arXiv:1202.1492 · Physical Review B

BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling

Lianyi He, Xu-Guang Huang

Published Jul 11, 2012• 29 citations
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Abstract

We present a systematic theoretical study of the BCS-BEC crossover problem in three-dimensional atomic Fermi gases at zero temperature with a spherical spin-orbit coupling which can be generated by a synthetic non-Abelian gauge field coupled to neutral fermions. Our investigations are based on the path-integral formalism, which is a powerful theoretical scheme for the study of the properties of the bound state, the superfluid ground state, and the collective excitations in the BCS-BEC crossover. At large spin-orbit coupling, the system enters the BEC state of a novel type of bound state (referred to as rashbon), which possesses a nontrivial effective mass. Analytical results and interesting universal behaviors for various physical quantities at large spin-orbit coupling are obtained. Our theoretical predictions can be tested in future experiments of cold Fermi gases with three-dimensional spherical spin-orbit coupling.

DOI
10.1103/physrevb.86.014511

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We present a systematic theoretical study of the BCS-BEC crossover problem in 3D atomic Fermi gases at zero temperature with a spherical spin-orbit coupling which can be realized by a synthetic non-Abelian gauge field coupled to fermions. Our investigations are based on the path integral formalism which is a powerful theoretical scheme for the study of the properties of bound state, the superfluid ground state, and the collective excitations in the BCS-BEC crossover. At large spin-orbit coupling, the system enters the BEC state of a novel type of bound state (referred to as rashbon) which possesses a non-trivial effective mass. Analytical results and interesting universal behaviors for various physical quantities at large spin-orbit coupling are obtained. Our theoretical predictions can be tested in future experiments of cold Fermi gases with 3D spherical spin-orbit coupling.

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We present a systematic theoretical study of the BCS-BEC crossover problem in three-dimensional atomic Fermi gases at zero temperature with a spherical spin-orbit coupling which can be generated by a synthetic non-Abelian gauge field coupled to neutral fermions. Our investigations are based on the path-integral formalism, which is a powerful theoretical scheme for the study of the properties of the bound state, the superfluid ground state, and the collective excitations in the BCS-BEC crossover. At large spin-orbit coupling, the system enters the BEC state of a novel type of bound state (referred to as rashbon), which possesses a nontrivial effective mass. Analytical results and interesting universal behaviors for various physical quantities at large spin-orbit coupling are obtained. Our theoretical predictions can be tested in future experiments of cold Fermi gases with three-dimensional spherical spin-orbit coupling.
We present a systematic theoretical study of the BCS-BEC crossover problem in 3D atomic Fermi gases at zero temperature with a spherical spin-orbit coupling which can be realized by a synthetic non-Abelian gauge field coupled to fermions. Our investigations are based on the path integral formalism which is a powerful theoretical scheme for the study of the properties of bound state, the superfluid ground state, and the collective excitations in the BCS-BEC crossover. At large spin-orbit coupling, the system enters the BEC state of a novel type of bound state (referred to as rashbon) which possesses a non-trivial effective mass. Analytical results and interesting universal behaviors for various physical quantities at large spin-orbit coupling are obtained. Our theoretical predictions can be tested in future experiments of cold Fermi gases with 3D spherical spin-orbit coupling.
We investigate the ground state of interacting spin-12\frac{1}{2}21​ fermions in three dimensions at a finite density ($\ensuremath{\rho}\ensuremath{\sim}{k}_{F}^{3}$) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector $\ensuremath{\lambda}\ensuremath{\equiv}({\ensuremath{\lambda}}_{x},{\ensuremath{\lambda}}_{y},{\ensuremath{\lambda}}_{z})$, whose magnitude $\ensuremath{\lambda}$ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length $({k}_{F}|{a}_{s}|\ensuremath{\lesssim}1)$, the ground state in the absence of the gauge field ($\ensuremath{\lambda}=0$) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum $(\ensuremath{\lambda}=0)$. For large gauge couplings $(\ensuremath{\lambda}/{k}_{F}\ensuremath{\gg}1)$, the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)---we call these bosons ``rashbons.'' In the absence of interactions (${a}_{s}={0}^{\ensuremath{-}}$), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling ${\ensuremath{\lambda}}_{T}$. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $\ensuremath{\lambda}$ near ${\ensuremath{\lambda}}_{T}$. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.
We present a systematic theoretical study of the BCS-BEC crossover in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). By solving the exact two-body problem in the presence of an attractive short-range interaction we show that the SOC enhances the formation of the bound state: the binding energy E(B) and effective mass m(B) of the bound state grows along with the increase of the SOC. For the many-body problem, even at weak attraction, a dilute Fermi gas can evolve from a BCS superfluid state to a Bose condensation of molecules when the SOC becomes comparable to the Fermi momentum. The ground-state properties and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature are studied, and analytical results are obtained in various limits. For large SOC, the BKT transition temperature recovers that for a Bose gas with an effective mass m(B). We find that the condensate and superfluid densities have distinct behaviors in the presence of SOC: the condensate density is generally enhanced by the SOC due to the increase of the molecule binding; the superfluid density is suppressed because of the nontrivial molecule effective mass m(B).
The recent experimental realization of spin-orbit coupling for ultracold atoms has generated much interest in the physics of spin-orbit-coupled degenerate Fermi gases. Although recently the BCS-BEC crossover in three-dimensional (3D) spin-orbit-coupled Fermi gases has been intensively studied, the corresponding two-dimensional (2D) crossover physics has remained unexplored. In this paper, we investigate, both numerically and analytically, the BCS-BEC crossover physics in 2D degenerate Fermi gases in the presence of the Rashba type of spin-orbit coupling. We derive the mean-field gap and atom-number equations suitable for 2D spin-orbit-coupled Fermi gases and solve them numerically and self-consistently, from which the dependence of the ground-state properties (chemical potential, superfluid pairing gap, ground-state energy per atom) on the system parameters (e.g., binding energy, spin-orbit-coupling strength) is obtained. Furthermore, we derive analytical expressions for these ground-state quantities, which agree well with our numerical results within a broad parameter region. Such analytical expressions also agree qualitatively with previous numerical results for 3D spin-orbit-coupled Fermi gases, where analytical results are lacking. We show that, with increasing spin-orbit coupling (SOC) strength, the chemical potential is shifted by a constant determined by the SOC strength. The superfluid pairing gap is enhanced significantly in the BCS limit for strong SOC, but increases only slightly in the BEC limit.
Upon increasing the strength of Rashba spin-orbit coupling $\ensuremath{\lambda}$, induced by a synthetic non-Abelian gauge field, a system of fermions at a finite density $\ensuremath{\rho}\ensuremath{\approx}{k}_{F}^{3}$ evolves to a BEC-like state [J. P. Vyasanakere, S. Zhang, and V. B. Shenoy, Phys. Rev. B 84, 014512 (2011)], even in the presence of a weak attractive interaction described by a scattering length as{a}_{s}as​. The BEC obtained at large spin-orbit coupling ($\ensuremath{\lambda}\ensuremath{\gg}{k}_{F}$) is a condensate of novel bosonic bound pairs of fermions (called ``rashbons'') whose properties are determined solely by the gauge field. Here we investigate the collective excitations of such superfluids by constructing a Gaussian theory using functional integral methods. We show that there is an emergent Galilean invariance at large $\ensuremath{\lambda}$, and the phase stiffness is determined by the rashbon density and mass, consistent with Leggett's theorem. We further demonstrate that the rashbon BEC (RBEC) is a superfluid of anisotropic rashbons interacting via a contact interaction characterized by a rashbon-rashbon scattering length aR{a}_{R}aR​. We show that aR{a}_{R}aR​ goes as ${\ensuremath{\lambda}}^{\ensuremath{-}1}$ and is essentially independent of the interaction between the fermions as long as it is nonzero. Analytical results are reported for high-symmetry gauge fields.
By adopting a TTT-matrix-based method within the G0G{G}_{0}GG0​G approximation for the pair susceptibility, we study the effects of the pairing fluctuation on the three-dimensional spin-orbit-coupled Fermi gases at finite temperature. The critical temperatures of the superfluid to normal phase transition are determined for three different types of spin-orbit coupling (SOC): (1) the extreme oblate (EO) or Rashba SOC, (2) the extreme prolate or equal Rashba-Dresselhaus SOC, and (3) the spherical (S) SOC. For EO- and S-type SOC, the SOC dependence of the critical temperature signals a crossover from BCS to BEC state; at strong SOC limit, the critical temperature recovers those of ideal BEC of rashbons. The pairing fluctuation induces a pseudogap in the fermionic excitation spectrum in both superfluid and normal phases. We find that, for EO- and S-type SOC, even at weak coupling, sufficiently strong SOC can induce sizable pseudogap. Our research suggests that the spin-orbit-coupled Fermi gases may open new means to the study of the pseudogap formation in fermionic systems.