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

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.