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We investigate thermodynamic properties and effects of quantum fluctuations in the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover region of a superfluid Fermi gas in the low-temperature limit. Including strong-coupling corrections within the framework of an extended T-matrix approximation, we numerically compute the isothermal compressibility $$\chi _n$$ . While quantum fluctuation effects on $$\chi _n$$ in the strong-coupling BEC regime are explained by the quantum depletion due to a repulsive interaction between tightly bound molecules, effects of self-energy shift on the Fermi chemical potential are found to enhance $$\chi _n$$ in the weak-coupling BCS region. We also show that the calculated $$\chi _n$$ agrees well with the recent experiment on a $$^6$$ Li Fermi gas done from the weak-coupling region to the unitarity limit. Our result would be useful for the study of many-body quantum corrections in the BCS-BEC crossover region of a strongly interacting Fermi superfluid. [ABSTRACT FROM AUTHOR]

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal phase. In the three-dimensional case, it has been shown that the so-called pseudogap phenomena can be well described by a (non-self-consistent) T-matrix approximation (TMA). In the two-dimensional case, while this strong-coupling theory can explain the pseudogap phenomenon in the strong-coupling regime, it unphysically gives large pseudogap size in the crossover region, as well as in the weak-coupling regime. We show that this difficulty can be overcome when one improves TMA to include higher-order pairing fluctuations within the framework of a self-consistent T-matrix approximation (SCTMA). The essence of this improvement is also explained. Since the observation of the BKT transition has recently been reported in a two-dimensional $$^6\hbox {Li}$$ Fermi gas, our results would be useful for the study of strong-coupling physics associated with this quasi-long-range order. [ABSTRACT FROM AUTHOR]

We theoretically investigate the shear viscosity $$\eta $$ , as well as the entropy density s, in the normal state of an ultracold Fermi gas. Including pairing fluctuations within the framework of a T-matrix approximation, we calculate these quantities in the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover region. We also evaluate $$\eta / s$$ , to compare it with the lower bound of this ratio, conjectured by Kovtun, Son, and Starinets (KSS bound). In the weak-coupling BCS side, we show that the shear viscosity $$\eta $$ is remarkably suppressed near the superfluid phase transition temperature $$T_{\mathrm{c}}$$ , due to the so-called pseudogap phenomenon. In the strong-coupling BEC side, we find that, within the neglect of the vertex corrections, one cannot correctly describe $$\eta $$ . We also show that $$\eta / s$$ decreases with increasing the interaction strength, to become very close to the KSS bound, $$\hbar /4\pi k_{\mathrm{B}}$$ , on the BEC side. [ABSTRACT FROM AUTHOR]

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal state. Including pairing fluctuations within the framework of a T-matrix approximation, we calculate the distribution function $$n({\varvec{Q}})$$ of Cooper pairs in terms of the center of mass momentum $${\varvec{Q}}$$ . In the strong-coupling regime, $$n({\varvec{Q}}=0)$$ is shown to exhibit a remarkable increase with decreasing the temperature in the low temperature region, which agrees well with the recent experiment on a two-dimensional $$^6$$ Li Fermi gas (Ries et al. in Phys Rev Lett 114:230401, ). Our result indicates that the observed remarkable increase of the number of Cooper pairs with zero center of mass momentum can be explained without assuming the Berezinskii-Kosterlitz-Thouless (BKT) transition, when one properly includes pairing fluctuations that are enhanced by the low-dimensionality of the system. Since the BKT transition is a crucial topic in two-dimensional Fermi systems, our results would be useful for the study toward the realization of this quasi-long-range order in an ultracold Fermi gas. [ABSTRACT FROM AUTHOR]