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arXiv:1107.2627 · Physical Review A

BCS-BEC crossover in spin-orbit-coupled two-dimensional Fermi gases

Gang Chen, Ming Gong, Chuanwei Zhang

Published Jan 3, 2012• 60 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.85.013601

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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.
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).
Extensive research has been lavished on the effects of spin-orbit couplings (SOCs) in attractively interacting Fermi systems in both neutral cold-atom systems and condensed-matter systems. Recently, it was suggested that a SOC drives a class of BCS to Bose-Einstein condensate (BEC) crossover that is different from the conventional one without a SOC. Here, we explore what are the most relevant physical quantities to describe such a BCS to BEC crossover and their experimental detections. We extend the concepts of the coherence length and ``Cooper-pair size'' in the absence of SOC to Fermi systems with SOC. We investigate the dependence of chemical potential, coherence length, and Cooper-pair size on the SOC strength and the scattering length at three dimensions (3D) (the bound-state energy at 2D) for three attractively interacting Fermi gases with 3D Rashba, 3D Weyl, and 2D Rashba SOC, respectively. We show that only the coherence length can be used to characterize this BCS to BEC crossover. Furthermore, it is the only length which can be directly measured by radio-frequency dissociation spectra type of experiments. We stress crucial differences among the coherence length, Cooper-pair size, and the two-body bound-state size. Our results provide the fundamental and global picture of the BCS to BEC crossover and its experimental detections in various cold-atom and condensed-matter systems.
Extensive research has been lavished on the effects of spin-orbit couplings (SOCs) in attractively interacting Fermi systems in both neutral cold-atom systems and condensed-matter systems. Recently, it was suggested that a SOC drives a class of BCS to Bose-Einstein condensate (BEC) crossover that is different from the conventional one without a SOC. Here, we explore what are the most relevant physical quantities to describe such a BCS to BEC crossover and their experimental detections. We extend the concepts of the coherence length and ``Cooper-pair size'' in the absence of SOC to Fermi systems with SOC. We investigate the dependence of chemical potential, coherence length, and Cooper-pair size on the SOC strength and the scattering length at three dimensions (3D) (the bound-state energy at 2D) for three attractively interacting Fermi gases with 3D Rashba, 3D Weyl, and 2D Rashba SOC, respectively. We show that only the coherence length can be used to characterize this BCS to BEC crossover. Furthermore, it is the only length which can be directly measured by radio-frequency dissociation spectra type of experiments. We stress crucial differences among the coherence length, Cooper-pair size, and the two-body bound-state size. Our results provide the fundamental and global picture of the BCS to BEC crossover and its experimental detections in various cold-atom and condensed-matter systems.
The recent experimental realization of spin-orbit coupled Fermi gases provides a unique opportunity to study the interplay between strong interaction and spin-orbit coupling (SOC) in a tunable, disorder-free system. We present here precision ab initio numerical results on the two-dimensional, unpolarized, uniform Fermi gas with attractive interactions and Rashba SOC. Using the auxiliary-field quantum Monte Carlo method and incorporating recent algorithmic advances, we carry out exact calculations on sufficiently large system sizes to provide accurate results systematically as a function of experimental parameters. We obtain the equation of state, the momentum distributions, the pseudospin correlations, and the pair wave functions. Our results help illuminate the rich pairing structure induced by SOC, and provide benchmarks for theory and guidance to future experimental efforts.
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.
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.