We theoretically present an economical and convenient way to study ground-state properties of a strongly interacting superfluid Fermi gas. Our strategy is that complicated strong-coupling calculations are used only to evaluate quantum fluctuation corrections to the chemical potential µ.Then, without any further strong-coupling calculations, we calculate the compressibility, sound velocity, internal energy, pressure, and Tan's contact, from the calculated µ without loss of accuracy, by using exact thermodynamic identities. Using a recent precise measurement of µ in a superfluid 6 Li Fermi gas, we show that an extended T -matrix approximation (ETMA) is suitable for our purpose, especially in the BCS-unitary regime, where our results indicate that many-body corrections are dominated by superfluid fluctuations. Since precise determinations of physical quantities are not always easy in cold Fermi gas physics, our approach would greatly reduce experimental and theoretical efforts toward the understanding of ground-state properties of this strongly interacting Fermi system.

We theoretically investigate strong-coupling properties of an ultracold Fermi gas in the BCS-BEC crossover regime in the non-equilibrium steady state, being coupled with two fermion baths. By developing a non-equilibrium strong-coupling theory based on the combined T -matrix approximation with the Keldysh Green's function technique, we show that the chemical potential bias applied by the two baths gives rise to the anomalous enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing fluctuations (although the system has no spin imbalance), resulting in the re-entrant behavior of the non-equilibrium superfluid phase transition in the BCS-unitary regime. These pairing fluctuations are also found to anomalously enhance the pseudogap phenomenon. Since various nonequilibrium phenomena have recently been measured in ultracold Fermi gases, our non-equilibrium strong-coupling theory would be useful to catch up this experimental development in this research field. :1910.12476v1 [cond-mat.quant-gas] arXiv

We theoretically investigate the shear viscosity η in the BCS-BEC crossover regime of an ultracold Fermi gas with a Feshbach resonance. Within the framework of the strong-coupling self-consistent T -matrix approximation, we examine how a strong pairing interaction associated with a Feshbach resonance affects this transport coefficient, in the normal state above the superfluid phase transition temperature T c . We show that, while η diverges in both the weak-coupling BCS and strong-coupling BEC limits, it becomes small in the unitary regime. The minimum of η is obtained, not at the unitarity, but slightly in the strong-coupling BEC side. This deviation is consistent with the recent experiment on a 6 Li Fermi gas. In the weak-coupling BCS regime, we also find that η exhibits anomalous temperature dependence near T c , which is deeply related to the pseudogap phenomenon originating form strong pairing fluctuations.

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