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arXiv:1202.5086 · Physical Review A

Pairing imbalance in the BCS-BEC crossover of an inhomogeneous three-component Fermi gas in two dimensions

Jia-jia Du, J.-Q. Liang, J.-Q. Liang

Published Mar 6, 2012• 4 citations
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Abstract

We in this paper investigate the phase diagram associated with the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover of a three-component ultracold superfluid Fermi gas of different chemical potentials and equal masses in two dimensions. The gap-order parameter and number densities are found analytically by using the functional-path-integral method. The balance of pairing will be broken in the free space due to the unequal chemical potentials. We obtain the same particle-number density and condensed fraction in the BCS-superfluid phase as those in a recent paper [Phys. Rev. A 83, 033630 (2011)] while the Sarma phase of the coexistence of normal and superfluid Fermi gases is characteristic of an inhomogeneous system. The minimum ratio of the BCS-superfluid phase becomes 1/3 in the BCS limit corresponding to the zero ratio in the two-component system in which the critical point of phase separation is ${\ensuremath{\epsilon}}_{B}/{\ensuremath{\epsilon}}_{F}=2$, but it becomes 3 in the three-component case.

DOI
10.1103/physreva.85.033610

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We in this paper investigate the phase diagram associated with the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover of a three-component ultracold superfluid Fermi gas of different chemical potentials and equal masses in two dimensions. The gap-order parameter and number densities are found analytically by using the functional-path-integral method. The balance of pairing will be broken in the free space due to the unequal chemical potentials. We obtain the same particle-number density and condensed fraction in the BCS-superfluid phase as those in a recent paper [Phys. Rev. A 83, 033630 (2011)] while the Sarma phase of the coexistence of normal and superfluid Fermi gases is characteristic of an inhomogeneous system. The minimum ratio of the BCS-superfluid phase becomes 1/3 in the BCS limit corresponding to the zero ratio in the two-component system in which the critical point of phase separation is \ensuremathϵB/\ensuremathϵF=2{\ensuremath{\epsilon}}_{B}/{\ensuremath{\epsilon}}_{F}=2\ensuremathϵB​/\ensuremathϵF​=2, but it becomes 3 in the three-component case.
In this paper, we investigate the condensate fraction (CF) of fermionic pairs in the BCS—BEC crossover for three-component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensional free space. By using the functional-path-integral method, we have analytically derived the number densities and bound-state energy, from which the off-diagonal long-range order is analyzed in terms of the asymptotic behavior of the two-body density matrix. The explicit formula of CF is obtained as a function of the bound-state energy and population imbalance. It is demonstrated that the CF spectrum with respect to the bound-state energy can be used to characterize the quantum phase transition between the two kinds of Sarma phases as well as the transition from three-component to two-component superfluid. Moreover we obtain the same analytic formula of CF in the BCS superfluid phase as that of homogeneous Fermi gas with equal chemical potentials.
We investigate the formation of Bose-Einstein condensation and a population imbalance in a three-component Fermi superfluid by increasing the U(3) invariant attractive interaction. We consider the system at zero temperature in three dimensions as well as in two dimensions. Within mean-field theory, we derive explicit formulas for the number densities, the gap order parameter, the condensate density, and the condensate fraction of the uniform system and analyze them in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of Cooper pairs to the Bose-Einstein condensate (BEC) of strongly bound molecular dimers. In addition we study this Fermi mixture trapped by a harmonic potential: We calculate the density profiles of the three components and the condensate density profile of Cooper pairs in the BCS-BEC crossover.
We analytically investigate superfluid phase in two dimension at zero temperature for asymmetric Fermi gas. Analytic expressions for both gap and chemical potentials at mean-field level are obtained as a function of binding energy and population imbalance when mass of different types of fermions is equal. We identify regions corresponding to normal, Sarma phase for different polarization, or mass ratio and discuss topological phase diagram in the BCS-BEC crossover and find that energy gap and chemical potential behave differently in these topological quantum phase. We also obtain the low-frequency and long-wavelength collective excitation spectrum and find sound velocity has a maximum when two types of mass are equal.
We study the zero temperature ground state of a two-dimensional atomic Fermi gas with chemical potential and population imbalance in the mean-field approximation. All calculations are performed in terms of the two-body binding energy B , whose variation allows one to investigate the evolution from the BEC to the BCS regimes. By means of analytical and exact expressions we show that, similarly to what is found in three dimensions, at fixed chemical potentials, BCS is the ground state until the critical imbalance h c , after which there is a first-order phase transition to the normal state. We find that h c , the Chandrasekhar–Clogston limit of superfluidity, has the same value as in three-dimensional systems. We show that for a fixed ratio B / F , where F is the two-dimensional Fermi energy, as the density imbalance m is increased from zero, the ground state evolves from BCS to phase separation to the normal state. At the critical imbalance m c , phase separation is not supported and the normal phase is energetically preferable. The BCS–BEC crossover is discussed in balanced and imbalanced configurations. Possible pictures of what may be found experimentally in these systems are also shown. We also investigate the necessary conditions for the existence of bound states in the balanced and imbalanced normal phase.
We investigate a two-component Fermi gas with unequal spin populations along the BCS-BEC crossover. By using the extended BCS equations and the concept of off-diagonal-long-range-order we derive a formula for the condensate number of Cooper pairs as a function of energy gap, average chemical potential, imbalance chemical potential and temperature. Then we study the zero-temperature condensate fraction of Cooper pairs by varying interaction strength and polarization, finding a depletion of the condensate fraction by increasing the population imbalance. We also consider explicitly the presence of an external harmonic confinement and we study, within the local-density approximation, the phase separation between superfluid and normal phase regions of the polarized fermionic cloud. In particular, we calculate both condensate density profiles and total density profiles from the inner superfluid core to the normal region passing for the interface, where a finite jump in the density is a clear manifestation of this phase-separated regime. Finally, we compare our theoretical results with the available experimental data on the condensate fraction of polarized 6Li atoms [Science 311, 492 (2006)]. These experimental data are in reasonable agreement with our predictions in a suitable range of polarizations, but only in the BCS side of the crossover up to unitarity.
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.