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arXiv:1910.12476 · Physical Review A

Nonequilibrium strong-coupling theory for a driven-dissipative ultracold Fermi gas in the BCS-BEC crossover region

Taira Kawamura, Ryo Hanai, Daichi Kagamihara, Daisuke Inotani, Yoji Ohashi

Published Jan 7, 2020• 15 citations
arXivHTMLPDF

Abstract

We theoretically investigate strong-coupling properties of an ultracold Fermi gas in the BCS-BEC crossover regime in the nonequilibrium steady state, being coupled with two fermion baths. By developing a nonequilibrium strong-coupling theory based on the combined $T$-matrix approximation with the Keldysh Green's function technique, we show that the chemical potential bias applied by the two baths gives rise to the anomalous enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing fluctuations (although the system has no spin imbalance), resulting in the re-entrant behavior of the nonequilibrium superfluid phase transition in the Bardeen-Cooper-Schrieffer unitary regime. These pairing fluctuations are also found to anomalously enhance the pseudogap phenomenon. Since various nonequilibrium phenomena have recently been measured in ultracold Fermi gases, our nonequilibrium strong-coupling theory would be useful to catch up with this experimental development in this research field.

DOI
10.1103/physreva.101.013602

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We theoretically investigate strong-coupling properties of an ultracold Fermi gas in the BCS-BEC crossover regime in the nonequilibrium steady state, being coupled with two fermion baths. By developing a nonequilibrium strong-coupling theory based on the combined TTT-matrix approximation with the Keldysh Green's function technique, we show that the chemical potential bias applied by the two baths gives rise to the anomalous enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing fluctuations (although the system has no spin imbalance), resulting in the re-entrant behavior of the nonequilibrium superfluid phase transition in the Bardeen-Cooper-Schrieffer unitary regime. These pairing fluctuations are also found to anomalously enhance the pseudogap phenomenon. Since various nonequilibrium phenomena have recently been measured in ultracold Fermi gases, our nonequilibrium strong-coupling theory would be useful to catch up with this experimental development in this research field.
Abstract We present a theoretical review of the recent progress in non-equilibrium BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover physics. As a paradigmatic example, we consider a strongly interacting driven-dissipative two-component Fermi gas where the non-equilibrium steady state is tuned by adjusting the chemical potential difference between two reservoirs that are coupled with the system. As a powerful theoretical tool to deal with this system, we employ the Schwinger-Keldysh Green’s function technique. We systematically evaluate the superfluid transition, as well as the single-particle properties, in the non-equilibrium BCS-BEC crossover region, by adjusting the chemical potential difference between the reservoirs and the strength of an s-wave pairing interaction associated with a Feshbach resonance. In the weak-coupling BCS side, the chemical potential difference is shown to imprint a two-step structure on the particle momentum distribution, leading to an anomalous enhancement of pseudogap, as well as the emergence of exotic Fulde-Ferrell-Larkin-Ovchinnikov-type superfluid instability. Since various non-equilibrium situations have recently been realized in ultracold Fermi gases, the theoretical understanding of non-equilibrium BCS-BEC crossover physics would become increasingly important in this research field.
We investigate magnetic properties and effects of pairing fluctuations in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu [Europhys. Lett. 75, 364 (2006)], and Parish et al. [Nat. Phys. 3, 124 (2007)], pointed out that the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem also exists in the ordinary non-self-consistent TTT-matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended TTT-matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a 6{}^{6}6Li Fermi gas done by Sanner et al. [Phys. Rev. Lett. 106, 010402 (2011)]. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below Tc{T}_{\mathrm{c}}Tc​ in the BCS-BEC crossover regime of cold Fermi gases.
We theoretically investigate the uniform spin susceptibility $\ensuremath{\chi}$ in the superfluid phase of an ultracold Fermi gas in the region of the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover. In our previous paper [H. Tajima et al., Phys. Rev. A 89, 033617 (2014)], including pairing fluctuations within an extended TTT-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where $\ensuremath{\chi}$ is anomalously suppressed even in the normal state near the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​. In this paper, we extend this work to the superfluid phase below Tc{T}_{\mathrm{c}}Tc​, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA $\ensuremath{\chi}$ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below Tc{T}_{\mathrm{c}}Tc​ in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a 6Li^{6}\mathrm{Li}6Li Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.
We investigate the uniform spin susceptibility ${\ensuremath{\chi}}_{\mathrm{s}}$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended TTT-matrix approximation, we show that ${\ensuremath{\chi}}_{\mathrm{s}}$ exhibits nonmonotonic temperature dependence in the normal state. In particular, ${\ensuremath{\chi}}_{\mathrm{s}}$ is suppressed near the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​ due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature Ts{T}_{\mathrm{s}}Ts​ as the temperature at which ${\ensuremath{\chi}}_{\mathrm{s}}$ takes a maximum value. Determining Ts{T}_{\mathrm{s}}Ts​ in the whole BCS-BEC crossover region, we identify the spin-gap regime in the phase diagram of a Fermi gas in terms of the temperature and the strength of a pairing interaction. We also clarify how the spin-gap phenomenon is related to the pseudogap phenomenon appearing in the single-particle density of states. Our results indicate that an ultracold Fermi gas in the BCS-BEC crossover region is a very useful system to examine the pseudogap phenomenon and the spin-gap phenomenon in a unified manner.
We theoretically investigate the recent photoemission-type experiment on 40^{40}40K Fermi gases done by JILA group. Including pairing fluctuations within a strong-coupling TTT-matrix theory, as well as effects of a harmonic trap within the local density approximation, we calculate photoemission spectra in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that the energy resolution of the current photoemission experiment is enough to detect the pseudogap phenomenon. We also show how the pseudogap in single-particle excitations continuously changes into the superfluid gap, as one decreases the temperature below the superfluid phase transition temperature. Our results would be useful for the study of single-particle properties of ultracold Fermi gases in the BCS-BEC crossover.
We theoretically investigate the recent photoemission-type experiment on40K Fermi gases done by JILA group. Including pairing fluctuations within a strong-coupling T-matrix theory, as well as effects of a harmonic trap within the local density approximation, we calculate photoemission spectra in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that the energy resolution of the current photoemission experiment is enough to detect the pseudogap phenomenon. We also show how the pseudogap in single-particle excitations continuously changes into the superfluid gap, as one decreases the temperature below the superfluid phase transition temperature. Our results would be useful for the study of single-particle properties of ultracold Fermi gases in the BCS-BEC crossover.