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arXiv:1706.05679 · Physical Review A

Spin susceptibility and effects of a harmonic trap in the BCS-BEC crossover regime of an ultracold Fermi gas

Hiroyuki Tajima, Ryo Hanai, Yoji Ohashi

Published Sep 11, 2017• 7 citations
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Abstract

We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation, as well as effects of a harmonic trap in the local density approximation, we calculate the local spin susceptibility ${\ensuremath{\chi}}_{\mathrm{t}}(r,T)$ in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation crossover region. We show that pairing fluctuations cause nonmonotonic temperature dependence of ${\ensuremath{\chi}}_{\mathrm{t}}(r,T)$. Although this behavior looks similar to the spin-gap phenomenon associated with pairing fluctuations in a uniform Fermi gas, the trapped case is found to also be influenced by the temperature-dependent density profile, in addition to pairing fluctuations. We demonstrate how to remove this extrinsic effect from ${\ensuremath{\chi}}_{\mathrm{t}}(r,T)$, to study the interesting spin-gap phenomenon purely originating from pairing fluctuations. Since experiments in cold-atom physics are always done in a trap, our results would be useful for the assessment of preformed pair scenario, from the viewpoint of spin-gap phenomenon.

DOI
10.1103/physreva.96.033614

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•Aug 17, 2016•1 citation
We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended TTT-matrix approximation, as well as effects of a harmonic trap in the local density approximation, we calculate the local spin susceptibility \ensuremathχt(r,T){\ensuremath{\chi}}_{\mathrm{t}}(r,T)\ensuremathχt​(r,T) in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation crossover region. We show that pairing fluctuations cause nonmonotonic temperature dependence of \ensuremathχt(r,T){\ensuremath{\chi}}_{\mathrm{t}}(r,T)\ensuremathχt​(r,T). Although this behavior looks similar to the spin-gap phenomenon associated with pairing fluctuations in a uniform Fermi gas, the trapped case is found to also be influenced by the temperature-dependent density profile, in addition to pairing fluctuations. We demonstrate how to remove this extrinsic effect from \ensuremathχt(r,T){\ensuremath{\chi}}_{\mathrm{t}}(r,T)\ensuremathχt​(r,T), to study the interesting spin-gap phenomenon purely originating from pairing fluctuations. Since experiments in cold-atom physics are always done in a trap, our results would be useful for the assessment of preformed pair scenario, from the viewpoint of spin-gap phenomenon.
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 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 theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined TTT-matrix theory with the local density approximation, we calculate strong-coupling corrections to single-particle local density of states (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, we clarify how the pseudogap structures in these quantities disappear with increasing the temperature. As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures T∗{T}^{*}T∗ and T∗∗{T}^{**}T∗∗ at which the pseudogap structures in these quantities completely disappear. Determining T∗{T}^{*}T∗ and T∗∗{T}^{**}T∗∗ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by the JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal-state properties of this strongly interacting Fermi system.
We investigate magnetic properties of an ultracold Fermi gas in the BCS (Bardeen-CooperSchrieffer)-BEC (Bose-Einstein condensation) crossover region. Using an extended T -matrix theory, we calculate the (pseudo)spin susceptibility χ in the normal state. In the crossover region, we show that the formation of preformed pairs naturally leads to non-monotonic temperature dependence of χ. Using this result, we introduce the spin-gap temperature T ∗ as the temperature at which χ takes a maximum value. In the BCS side, this characteristic temperature is found to be close to the temperature at which the density of states at ω = 0 starts to be suppressed by pairing fluctuations. Since the existence of the pseudogap is still controversial in ultracold Fermi gases, our results would be helpful to resolve this fundamental problem.
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 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.