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Journal of the Optical Society of America B

Comparative study of the condensate fraction of balanced and imbalanced uniform fermionic systems in the BEC-BCS crossover

Shahzeb Aziz, Sidra Jamil, Abdul Rahman, Imrana Ashraf

Published Dec 23, 2019• 0 citations
Publisher

Abstract

In this paper, we have made a comparative study of the condensate fraction of balanced and imbalanced two-component uniform fermionic systems in the Bose–Einstein condensation-Bardeen–Cooper–Schrieffer (BEC-BCS) crossover. We have used extended BCS equations to calculate the condensate fraction of Cooper pairs as a function of chemical potential and gap energy in a balanced system using a path integral approach. For an imbalanced system, the same equation has been derived as a function of average chemical potential, imbalanced chemical potential, gap energy, and temperature. The condensate fraction in a balanced fermionic system varies with the interaction parameter, whereas its behavior in an imbalanced system changes with the interaction parameter and polarization, in different regimes. In particular, the effect of polarization on the condensate fraction has been studied in an imbalanced system for odd values of polarization. We have compared the condensate fraction for both systems analytically and graphically and observed that for an imbalanced system, it decreases with increasing polarization and almost vanishes for higher values of polarization in the BEC regime.

DOI
10.1364/josab.377423

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In this paper, we have made a comparative study of the condensate fraction of balanced and imbalanced two-component uniform fermionic systems in the Bose–Einstein condensation-Bardeen–Cooper–Schrieffer (BEC-BCS) crossover. We have used extended BCS equations to calculate the condensate fraction of Cooper pairs as a function of chemical potential and gap energy in a balanced system using a path integral approach. For an imbalanced system, the same equation has been derived as a function of average chemical potential, imbalanced chemical potential, gap energy, and temperature. The condensate fraction in a balanced fermionic system varies with the interaction parameter, whereas its behavior in an imbalanced system changes with the interaction parameter and polarization, in different regimes. In particular, the effect of polarization on the condensate fraction has been studied in an imbalanced system for odd values of polarization. We have compared the condensate fraction for both systems analytically and graphically and observed that for an imbalanced system, it decreases with increasing polarization and almost vanishes for higher values of polarization in the BEC regime.
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 the Bose-Einstein condensation of fermionic pairs in a uniform two-component Fermi gas, obtaining an explicit formula for the condensate density as a function of the chemical potential and the energy gap. We analyze the condensate fraction in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly interacting Cooper pairs to the Bose-Einstein condensate of molecular dimers. By using the local-density approximation we study confined Fermi vapors of alkali-metal atoms for which there is experimental evidence of condensation also on the BCS side of the Feshbach resonance. Our theoretical results are in agreement with these experimental data and give the behavior of the condensate on both sides of the Feshbach resonance at zero temperature.
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.
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) in a relativistic superfluid within a boson-fermion model. The model includes, besides the fermions, separate bosonic degrees of freedom, accounting for the bosonic nature of the Cooper pairs. The crossover is realized by tuning the difference between the boson mass and boson chemical potential as a free parameter. The model yields populations of condensed and uncondensed bosons as well as gapped and ungapped fermions throughout the crossover region for arbitrary temperatures. Moreover, we observe the appearance of antiparticles for sufficiently large values of the crossover parameter. As an application, we study pairing of fermions with imbalanced populations. The model can potentially be applied to color superconductivity in dense quark matter at strong couplings.
We investigate the Bose-Einstein condensation of fermionic pairs in a two-dimensional uniform two-component Fermi superfluid obtaining an explicit formula for the condensate density as a function of the chemical potential and the energy gap. By using the mean-field extended Bardeen-Cooper-Schrieffer theory, we analyze, as a function of the bound-state energy, the off-diagonal long-range order in the crossover from the Bardeen-Cooper-Schrieffer state of weakly bound Cooper pairs to the Bose-Einstein condensate of strongly-bound molecular dimers.
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.