Abstract:
We determine the conditions under which superfluidity with and without quantized vortices appears in a weakly interacting two-component atomic Fermi gas that is trapped in a rotating cylindrical symmetric harmonic potential. We compute the phase diagram as a function of rotation frequency, scattering length, temperature, total number of trapped atoms, and population imbalance.

Abstract:
The pairing of fermions is at the heart of superconductivity and superfluidity. The recent experimental realization of strongly interacting atomic Fermi gases has opened a new, controllable way to study novel forms of pairing and superfluidity. A major controversial issue has been the stability of superfluidity against an imbalance between the two spin components when the fermions interact resonantly. Here we present the phase diagram of a spin-polarized Fermi gas of $^6$Li atoms at unitarity, mapping out the superfluid phase versus temperature and density imbalance. Using tomographic techniques, we reveal spatial discontinuities in the spin polarization, the signature of a first-order superfluid-to-normal phase transition, which disappears at a tricritical point where the nature of the phase transition changes from first-order to second-order. At zero temperature, there is a quantum phase transition from a fully-paired superfluid to a partially-polarized normal gas. These observations and the implementation of an in situ ideal gas thermometer provide quantitative tests of theoretical calculations on the stability of resonant superfluidity.

Abstract:
We investigate the superfluid phase transition and single-particle excitations in the BCS (Bareen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas with mass imbalance. In our recent paper [R. Hanai, et. al., Phys. Rev. A 88, 053621 (2013)], we showed that an extended $T$-matrix approximation (ETMA) can overcome the serious problem known in the ordinary (non-self-consistent) $T$-matrix approximation that it unphysically gives double-valued superfluid phase transition temperature $T_{\rm c}$ in the presence of mass imbalance. However, at the same time, the ETMA was also found to give the vanishing $T_{\rm c}$ in the weak-coupling and highly mass-imbalanced case. In this paper, we inspect the correctness of this ETMA result, using the self-consistent $T$-matrix approximation (SCTMA). We show that the vanishing $T_{\rm c}$ is an artifact of the ETMA, coming from an internal inconsistency of this theory. The superfluid phase transition actually always occurs, irrespective of the ratio of mass imbalance. We also apply the SCTMA to the pseudogap problem in a mass-imbalanced Fermi gas. We show that pairing fluctuations induce different pseudogap phenomena between the the light component and heavy component. We also point out that a $^6$Li-$^{40}$K mixture is a useful system for the realization of a hetero pairing state, as well as for the study of component-dependent pseudogap phenomena.

Abstract:
We in this paper investigate the phase diagram associated with the BCS-BEC crossover of a three-component ultracold superfluid-Fermi-gas of different chemical-potentials and equal masses in two dimensions. The gap order parameter and number densities are found analytically by using the functional path-integral method. The balance of paring will be broken in the free space due to the unequal chemical-potentials. We obtain the same particle number-density and condensed fraction in the BCS superfluid phase as that in a recent paper (Phys. Rev. A 83, 033630), while the Sarma phase of coexistence of normal and superfluid Fermi gases is the characteristics of inhomogeneous system. The minimum ratio of BCS superfluid phase becomes 1/3 in the BCS limit corresponding to the zero-ratio in the two-component system in which the critical point of phase separation is {\epsilon}B/{\epsilon}F = 2 but becomes 3 in the three-component case.

Abstract:
We analyze the zero temperature phase diagram for an asymmetric two-component Fermi gas as a function of mass anisotropy and population imbalance. We identify regions corresponding to normal, or uniform/non-uniform superfluid phases, and discuss topological quantum phase transitions in the Bardeen-Cooper-Schrieffer (BCS), unitarity and Bose-Einstein condensation (BEC) limits. Lastly, we derive the zero temperature low frequency and long wavelength collective excitation spectrum, and recover the Bogoliubov relation for weakly interacting dilute bosons in the BEC limit.

Abstract:
We construct the phase diagram of a homogeneous two component Fermi gas with population imbalance under a Feshbach resonance. In particular, we study the physics and stability of the Larkin-Ovchinnikov phase. We show that this phase is stable over a much larger parameter range than what has been previously reported by other authors.

Abstract:
We consider a trapped Fermi gas with population imbalance at finite temperatures and map out the detailed phase diagram across a wide Feshbach resonance. We take the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state into consideration and minimize the thermodynamical potential to ensure stability. Under the local density approximation, we conclude that a stable LOFF state is present only on the BCS side of the Feshbach resonance, but not on the BEC side or at unitarity. Furthermore, even on the BCS side, a LOFF state is restricted at low temperatures and in a small region of the trap, which makes a direct observation of LOFF state a challenging task.

Abstract:
We investigate the phase diagram and the BCS-BEC crossover of a homogeneous three-component ultracold Fermi gas with a U(3) invariant attractive interaction. We show that the system at sufficiently low temperatures exhibits population imbalance, as well as fermionic pairing. We describe the crossover in this system, connecting the weakly interacting BCS regime of the partially population-imbalanced fermion pairing state and the BEC limit with three weakly interacting species of molecules, including pairing fluctuations within a t-matrix calculation of the particle self-energies.

Abstract:
We derive the underlying finite temperature theory which describes Fermi gas superfluidity with population imbalance in a homogeneous system. We compute the pair formation temperature and superfluid transition temperature $T_c$ and superfluid density in a manner consistent with the standard ground state equations, and thereby present a complete phase diagram. Finite temperature stabilizes superfluidity, as manifested by two solutions for $T_c$, or by low $T$ instabilities. At unitarity the polarized state is an ``intermediate temperature superfluid".

Abstract:
We study two-component (or pseudo-spin-1/2) Bose or Fermi gases in one dimension, in which particles are convertible between the components. Through bosonization and numerical analyses of a simple lattice model, we demonstrate that, in such gases, a strong intercomponent repulsion induces spontaneous population imbalance between the components, namely, the ferromagnetism of the pseudo spins. The imbalanced phase contains gapless charge excitations characterized as a Tomonaga-Luttinger liquid and gapped spin excitations. We uncover a crucial effect of the intercomponent particle hopping on the transition to the imbalanced phase. In the absence of this hopping, the transition is of first order. At the transition point, the energy spectrum reveals certain degeneracy indicative of an emergent SU(2) symmetry. With an infinitesimal intercomponent hopping, the transition becomes of Ising type. We determine the phase diagram of the model accurately and test the reliability of the weak-coupling bosonization formalism.