We investigate the center-of-mass momentum distribution ${n}_{\mathbit{Q}}$ of Cooper pairs and their first-order correlation function
g1(r) in a strongly interacting two-dimensional Fermi gas. Recently, the Berezinskii-Kosterlitz-Thouless (BKT) transition was reported in a two-dimensional
6Li Fermi gas, based on (1) the observations of anomalous enhancement of ${n}_{\mathbit{Q}=\mathbit{0}}$ [Ries et al., Phys. Rev. Lett. 114, 230401 (2015)] , as well as (2) a power-law behavior of
g1(r) [Murthy et al., Phys. Rev. Lett. 115, 010401 (2015)]. However, including pairing fluctuations within a
T-matrix approximation (TMA), we show that these results can still be explained as strong-coupling properties of a normal-state two-dimensional Fermi gas. Our results indicate the importance of further experimental observations, to definitely confirm the realization of the BKT transition in this system. Since the BKT transition has been realized in a two-dimensional ultracold Bose gas, our results would be useful for the achievement of this quasi-long-range order in an ultracold Fermi gas.
The density of states of Fermi gas and density of states of Cooper pairs that form Boson Condensate have been compared. The derived density of states of Fermi gas is elucidated using literature in a cube of size L [1]. In this line, Cooper pairs are highly coherent and responsible for super conductivity[2]. The Cooper pairs form Boson-Einstein condensate of spin quantum number s-1[3], we obtained its density of states. The ratio of Cooper pair density of states to Fermi gas density of states has been derived. To obtain the relation between the two densities of states, the condition of high coherent Cooper pairs in Bose-Einstein condensate has been taken in to account. In addition, the fact that Fermions do not take same quantum states was employed while highly coherent Cooper pairs with s-1 do take same quantum states for they are Boson particles.