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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 theoretically investigate the normal state properties of a Bose-Fermi mixture with a strong attractive interaction between Fermi and Bose atoms. We extend the ordinary T-matrix approximation (TMA) with respect to Bose-Fermi pairing fluctuations, to include the Hugenholtz-Pines' relation for all Bose Green's functions appearing in TMA self-energy diagrams. This extension is shown to be essentially important to correctly describe the physical properties of the Bose-Fermi mixture, especially near the Bose-Einstein condensation instability. Using this improved TMA, we clarify how the formation of composite fermions affects Bose and Fermi single-particle excitation spectra, over the entire interaction strength. [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 the superfluid phase transition and effects of mass imbalance in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an cold Fermi gas. We point out that the Gaussian fluctuation theory developed by Nozières and Schmitt-Rink and the T-matrix theory, that are now widely used to study strong-coupling physics of cold Fermi gases, give unphysical results in the presence of mass imbalance. To overcome this problem, we extend the T-matrix theory to include higher-order pairing fluctuations. Using this, we examine how the mass imbalance affects the superfluid phase transition. Since the mass imbalance is an important key in various Fermi superfluids, such as K-Li Fermi gas mixture, exciton condensate, and color superconductivity in a dense quark matter, our results would be useful for the study of these recently developing superfluid systems. [ABSTRACT FROM AUTHOR]

Abstract  We study pseudogap behaviors of ultracold Fermi gases in the BCS-BEC crossover region. We calculate the density of states (DOS), as well as the single-particle spectral weight, above the superfluid transition temperature T c including pairing fluctuations within a T-matrix approximation. We find that DOS exhibits a pseudogap structure in the BCS-BEC crossover region, which is most remarkable near the unitarity limit. We determine the pseudogap temperature T * at which the pseudogap structure in DOS disappears. We also introduce another temperature T ** at which the BCS-like double-peak structure disappears in the spectral weight. While one finds T *>T ** in the BCS regime, T ** becomes higher than T * in the crossover and BEC regime. We also determine the pseudogap region in the phase diagram in terms of temperature and pairing interaction. [ABSTRACT FROM AUTHOR]