Momentum distribution of Cooper-pairs and strong-coupling effects in a two-dimensional Fermi gas near the Berezinskii-Kosterlitz-Thouless transition

摘要

We investigate strong-coupling properties of a two-dimensional ultracoldFermi gas in the normal state. Including pairing fluctuations within theframework of a $T$-matrix approximation, we calculate the distribution function$n({\boldsymbol Q})$ of Cooper pairs in terms of the center of mass momentum${\boldsymbol Q}$. In the strong-coupling regime, $n({\boldsymbol Q}=0)$ isshown to exhibit a remarkable increase with decreasing the temperature in thelow temperature region, which agrees well with the recent experiment on atwo-dimensional $^6$Li Fermi gas [M. G. Ries, {\it et. al.}, Phys. Rev. Lett.{\bf 114}, 230401 (2015)]. Our result indicates that the observed remarkableincrease of the number of Cooper pairs with zero center of mass momentum can beexplained without assuming the Berezinskii-Kosterlitz-Thouless (BKT)transition, when one properly includes pairing fluctuations that are enhancedby the low-dimensionality of the system. Since the BKT transition is a crucialtopic in two-dimensional Fermi systems, our results would be useful for thestudy toward the realization of this quasi-long-range order in an ultracoldFermi gas.