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arXiv:1208.1455 · Physical Review A

Exotic phase separation and phase diagrams of a Fermi-Fermi mixture in a trap at finite temperature

Jibiao Wang, Hao Guo, Qijin Chen

Published Apr 11, 2013• 13 citations
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Abstract

The pairing and superfluid phenomena in a two-component Fermi gas can be strongly affected by the population and mass imbalances. Here we present phase diagrams of an atomic Fermi-Fermi mixture as they undergo BCS--Bose-Einstein condensation (BEC) crossover using a pairing fluctuation theory. We focus on the finite temperature and trap effects, with an emphasis on the mixture of ${}^{6}$Li and ${}^{40}$K. We show that there exist exotic types of phase separation in the (near-)BEC regime, associated with a pseudogap effect. Moreover, in the BCS and unitary regimes, the spatial density and gap profiles exhibit sandwichlike shell structures with superfluid or pseudogapped normal state in the middle shell. Such a sandwichlike shell structure appears when the mass imbalance increases beyond a certain threshold. Our result is relevant to future experiments on the ${}^{6}$Li-${}^{40}$K and other possible Fermi-Fermi mixtures.

DOI
10.1103/physreva.87.041601

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•Jan 1, 2013•0 citations
The pairing and superfluid phenomena in a two-component Fermi gas can be strongly affected by the population and mass imbalances. Here we present phase diagrams of an atomic Fermi-Fermi mixture as they undergo BCS--Bose-Einstein condensation (BEC) crossover using a pairing fluctuation theory. We focus on the finite temperature and trap effects, with an emphasis on the mixture of 6{}^{6}6Li and 40{}^{40}40K. We show that there exist exotic types of phase separation in the (near-)BEC regime, associated with a pseudogap effect. Moreover, in the BCS and unitary regimes, the spatial density and gap profiles exhibit sandwichlike shell structures with superfluid or pseudogapped normal state in the middle shell. Such a sandwichlike shell structure appears when the mass imbalance increases beyond a certain threshold. Our result is relevant to future experiments on the 6{}^{6}6Li-40{}^{40}40K and other possible Fermi-Fermi mixtures.
We study the finite temperature TTT behavior of trapped Fermi gases as they undergo BCS--Bose-Einstein condensation (BEC) crossover, in the presence of a population imbalance. Our results, in qualitative agreement with recent experiments, show how the superfluid phase transition is directly reflected in the particle density profiles. We demonstrate that at $T\ensuremath{\ne}0$ and in the near-BEC and unitary regimes, the polarization is excluded from the superfluid core. Importantly, a substantial polarization fraction is carried by a normal region of the trap having strong pair correlations, which we associate with noncondensed pairs or the ``pseudogap phase.''
We study the mass imbalanced Fermi-Fermi mixture within the framework of a two-dimensional lattice fermion model. Based on the thermodynamic and species-dependent quasiparticle behavior, we map out the finite-temperature phase diagram of this system and show that unlike the balanced Fermi superfluid, there are now two different pseudogap regimes as PG-I and PG-II. While within the PG-I regime both the fermionic species are pseudogapped, PG-II corresponds to the regime where pseudogap feature survives only in the light species. We believe that the single-particle spectral features that we discuss in this paper are observable through the species-resolved radio-frequency spectroscopy and momentum-resolved photoemission spectroscopy measurements on systems such as ${6}_{\text{Li}}\text{\ensuremath{-}}{40}_{\text{K}}$ mixture. We further investigate the interplay between the population and mass imbalances and report that at a fixed population imbalance, the BCS-BEC crossover in a Fermi-Fermi mixture would require a critical interaction (Uc{U}_{c}Uc​) for the realization of the uniform superfluid state. The effect of imbalance in mass on the exotic Fulde-Ferrell-Larkin-Ovchinnikov superfluid phase has been probed in detail in terms of the thermodynamic and quasiparticle behavior of this phase. It has been observed that in spite of the sss-wave symmetry of the pairing field, a nodal superfluid gap is realized in the Larkin-Ovchinnikov regime. Our results on the various thermal scales and regimes are expected to serve as benchmarks for the experimental observations on ${6}_{\text{Li}}\text{\ensuremath{-}}{40}_{\text{K}}$ mixture.
We investigate strong pairing fluctuations and effects of a harmonic trap in the superfluid phase of an ultracold Fermi gas. Including amplitude and phase fluctuations of the inhomogeneous superfluid order parameter $\ensuremath{\Delta}(r)$ in a trap within a combined TTT-matrix theory with the local density approximation, we examine local properties of single-particle excitations and a thermodynamic quantity in the BCS-BEC crossover region. Below the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, we show that inhomogeneous pairing fluctuations lead to a shell structure of the gas cloud in which the spatial region where the ordinary BCS-type superfluid density of states appears surrounded by the region where the pseudogap associated with strong pairing fluctuations dominates single-particle excitations. The former spatial region enlarges to eventually cover the whole gas cloud far below Tc{T}_{\mathrm{c}}Tc​. We also examine how this shell structure affects the photoemission spectrum, as well as the local pressure. Since a cold Fermi gas is always trapped in a harmonic potential, our results would be useful for the study of strong-coupling superfluid physics, including this realistic situation.
We investigate single-particle properties of a mass-imbalanced Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)--BEC (Bose-Einstein condensation) crossover region. In the presence of mass imbalance, we point out that the ordinary TTT-matrix approximation, which has been extensively used to clarify various BCS-BEC crossover physics in the mass-balanced case, unphysically gives a double-valued solution in terms of the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​ in the crossover region. To overcome this serious problem, we include higher order strong-coupling corrections beyond the TTT-matrix level. Using this extended TTT-matrix theory, we calculate single-particle excitations in the normal state above Tc{T}_{\mathrm{c}}Tc​. The so-called pseudogap phenomena originating from pairing fluctuations are shown to be different between the light-mass component and heavy-mass component, which becomes more remarkable at higher temperatures. Since Fermi condensates with hetero-Cooper pairs have recently been discussed in various fields, such as exciton (polariton) condensates as well as color superconductivity, our results would be useful for the further development of Fermi superfluid physics, beyond the conventional superfluid state with homo-Cooper pairs.
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.
an atomic mass in the -component) in the BCS-BEC crossover region. Including pairing fluctuations within a self-consistent T -matrix theory, we examine how the superfluid instability is affected by the presence of mass imbalance. We determine the superfluid region in the phase diagram of a Fermi gas in terms of the temperature, the strength of a pairing interaction, and the ratio of mass imbalance. The superfluid phase transition is shown to always occur even when m m#. 2 This behavior of Tc is quite different from the previous result in an extended T -matrix theory, 3 where Tc vanishes at a certain value of m=m# > 0 in the BCS regime. Since Fermi condensates with mass imbalance have been discussed in various systems, such as a cold Fermi gas, an exciton(polariton) condensate, as well as color superconductivity, our results would be useful for further understandings of these novel Fermi superfluids.