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.

中文翻译：

---

BEC-BCS分频器中平衡和不平衡均匀铁离子系统凝结水分数的比较研究

在本文中，我们对Bose-Einstein缩合-Bardeen-Cooper-Schrieffer（BEC-BCS）交换中平衡和不平衡的两组分均匀铁电体系的凝结分数进行了比较研究。我们使用扩展的BCS方程，使用路径积分方法，计算了平衡系统中Cooper对的冷凝分数与化学势和能隙的关系。对于不平衡系统，已经根据平均化学势，不平衡化学势，能隙能量和温度得出了相同的方程。平衡的铁电体系中的冷凝物分数随相互作用参数而变化，而在不平衡的系统中其行为随相互作用参数和极化而变化，在不同的状态下。特别是，在奇数极化值的不平衡系统中，研究了极化对冷凝物馏分的影响。我们通过分析和图形比较了两种系统的凝结水分数，并观察到对于不平衡的系统，其凝结水分数随着极化的增加而降低，而在BEC体制中，对于更高的极化值几乎消失了。