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arXiv:1109.3970

Condensate Fraction and Pair Coherence Lengths of Two-Dimension Fermi Gases with Spin-Orbit Coupling

Beibing Huang, Shaolong Wan

Published Sep 19, 2011• 0 citations
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Abstract

The effects of Rashba spin-orbit coupling on BCS-BEC crossover, the condensate fraction and pair coherence lengths for a two-component attractive Fermi gas in two dimension are studied. The results at $T=0K$ indicate that (1) when the strength of SOC is beyond a critical value, BCS-BEC crossover does not happen in a conventional sense; (2) SOC enhances the condensate fraction, but suppresses pair coherence lengths.

DOI
10.48550/arxiv.1109.3970

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The effects of Rashba spin-orbit coupling on BCS-BEC crossover, the condensate fraction and pair coherence lengths for a two-component attractive Fermi gas in two dimension are studied. The results at T=0KT=0KT=0K indicate that (1) when the strength of SOC is beyond a critical value, BCS-BEC crossover does not happen in a conventional sense; (2) SOC enhances the condensate fraction, but suppresses pair coherence lengths.
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.
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).
We investigate the pair condensation of a two-spin-component Fermi gas in the presence of both Rashba and Dresselhaus spin-orbit couplings. We calculate the condensate fraction in the BCS-BEC crossover both in two and in three dimensions by taking into account singlet and triplet pairings. These quantities are studied by varying the spin-orbit interaction from the case with the only Rashba to the equal-Rashba-Dresselhaus one. We find that, by mixing the two couplings, the singlet pairing decreases while the triplet pairing is suppressed in the BCS regime and increased in the BEC regime, both in two and three dimensions. At fixed spin-orbital strength, the greatest total condensate fraction is obtained when only one coupling (only Rashba or only Dresselhaus) is present.
We investigate the pair condensation of a two-spin-component Fermi gas in the presence of both Rashba and Dresselhaus spin-orbit couplings. We calculate the condensate fraction in the BCS-BEC (Bardeen-Cooper-Schrieffer--Bose-Einstein condensate) crossover in both two and three dimensions by taking into account singlet and triplet pairings. These quantities are studied by varying the spin-orbit interaction from the case with the only-Rashba to the equal-Rashba-Dresselhaus one. We find that by mixing the two couplings, the singlet pairing decreases while the triplet pairing is suppressed in the BCS regime and increased in the BEC regime, both in two and three dimensions. At fixed spin-orbital strength, the greatest total condensate fraction is obtained when only one coupling (only Rashba or only Dresselhaus) is present.
We study the effects of laser-induced Rashba-like spin-orbit coupling along the Bardeen-Cooper-Schrieffer--Bose-Einstein condensate (BCS-BEC) crossover of a Feshbach resonance for a two-spin-component Fermi gas. We calculate the condensate fraction in three and two dimensions and find that this quantity characterizes the crossover better than other quantities, like the chemical potential or the pairing gap. By considering both the singlet and the triplet pairings, we calculate the condensate fraction and show that a large-enough spin-orbit interaction enhances the singlet condensate fraction in the BCS side while suppressing it on the BEC side.