The density distributions of the two components of a trapped, ultracold Fermi gas with population imbalance reveal the effect of imbalance on superfluid pairing. We develop a path-integral derivation of the density, that takes into account both fluctuations beyond mean-field and effects of nonzero temperature. The calculated density profiles compare favorably to the measured density profiles, and illustrate the necessity to incorporate both quantum fluctuations and finite temperature effects. The temperature dependence of the density profiles, especially near the superfluid-normal interface, allows for determining the temperature of the superfluid core in current experiments.
We study the finite temperature
T behavior of trapped Fermi gases as they undergo BCS--Bose-Einstein condensation (BEC) crossover, in the presence of a population imbalance. Our results, in qualitative agreement with recent experiments, show how the superfluid phase transition is directly reflected in the particle density profiles. We demonstrate that at $T\ensuremath{\ne}0$ and in the near-BEC and unitary regimes, the polarization is excluded from the superfluid core. Importantly, a substantial polarization fraction is carried by a normal region of the trap having strong pair correlations, which we associate with noncondensed pairs or the ``pseudogap phase.''
We investigate the temperature effects in an imbalanced superfluid atomic Fermi gas. We consider a bilayer system of two-component dipolar fermionic atoms with one layer containing atoms of one component and the other layer the atoms of other component with an imbalance between the populations of the two components. This imbalance results in uniform and nonuniform superfluid phases such as phase-separated BCS, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma and normal Fermi liquid phases for different system parameters. Using the mean-field BCS theory together with the superfluid mass-density criterion we classify different phases in thermodynamic phase diagram. Our results indicate that for a dipolar Fermi system the Sarma phase is stable for large imbalance at finite temperature below the critical temperature, and the FFLO phase is stable for intermediate imbalance on the BCS side of a BCS-BCE crossover. The phase diagram in the temperature and population imbalance plane indicate three Lifshitz points: one corresponding to coexistance of BCS, FFLO and normal Fermi liquid phase while the other two correspond to the coexistance of the Sarma phase, FFLO phase and normal Fermi phase for dipolar interactions.
Motivated by recent experiments in trapped Fermi gas with spin population imbalance, we discuss the effects of the quantum and thermal fluctuations of the interface between a fully paired superfluid core and a fully polarized Fermi gas. We demonstrate that even if there is no true partially polarized thermodynamic phase in bulk, the interface fluctuation can give rise to a partially polarized transition regime in trap. Our theory yields a definite prediction for the functional forms of the spatial profile of spin polarization and pairing gap, and we show that the spin-resolved density profiles measured by both the MIT and Rice groups obey this function form. We also show that sufficient large fluctuation will lead to a visibly unequal density even at the center of the cloud. We hope this picture can shed lights on the controversial discrepancies in recent experiments.
On the basis of the phase diagram of the uniform system, we calculate the density profiles of a trapped polarized Fermi gas at zero temperature using the local density approximation. By varying the overall polarization and the interaction strength, we analyze the appearance of a discontinuity in the profile, signaling a first-order phase transition from a superfluid inner core to a normal outer shell. The local population imbalance between the two components and the size of the various regions of the cloud corresponding to different phases are also discussed. The calculated profiles are quantitatively compared with the ones recently measured by Shin et al. [Phys. Rev. Lett. 101, 070404 (2008)].
A detailed description is given of the phase diagram for a two-component unitary Fermi gas with mass and population imbalance, for both homogeneous and trapped systems. This aims at providing quantitative benchmarks for the normal-to-superfluid phase transition of a mass-imbalanced Fermi gas in the temperature-polarization parameter space. A self-consistent
t-matrix approach is adopted, which has already proven to accurately describe the thermodynamic properties of the mass- and population-balanced unitary Fermi gas. Our results provide a guideline for the ongoing experiments on heteronuclear Fermi mixtures.
We address the thermodynamics, density profiles, and superfluid density of trapped fermions undergoing BCS-BEC crossover. We consider the case of zero and finite population imbalance and apply the local density approximation (LDA) to include the trap potential. Our approach represents a fully self-consistent treatment of ``pseudogap effects.'' These effects reflect the distinction between the pair formation temperature
T∗ and the pair condensation temperature
Tc. As a natural corollary, this temperature difference must be accommodated in the fermionic excitation spectrum
Ek to reflect the fact that fermions are paired at and above
Tc. It is precisely this natural corollary which has been omitted from all other many body approaches in the literature. At a formal level, we show how enforcing this corollary implies that pairing fluctuation or self-energy contributions enter into both the gap and the number equations; this is necessary in order to be consistent with a generalized Ward identity. At a less formal level, we demonstrate that we obtain physical results for the superfluid density
ns(T) at all temperatures. In contrast, previous work in the literature has led to nonmonotonic, or multivalued or discontinuous behavior for
ns(T). Because it reflects the essence of the superfluid state, we view the superfluid density as a critical measure of the physicality of a given crossover theory. In a similarly unique fashion, we emphasize that in order to properly address thermodynamic properties of a trapped Fermi gas, a necessary first step is to demonstrate that the particle density profiles are consistent with experiment. Without a careful incorporation of the distinction between the pairing gap and the order parameter, the LDA-derived density profiles (of the unpolarized gas) tend to exhibit sharp features at the condensate edge, which are never seen experimentally in the crossover regime. The lack of demonstrable consistency between theoretical and experimental density profiles, along with problematic behavior found for the superfluid density, casts doubt on previous claims in the literature concerning quantitative agreement between thermodynamical calculations and experiment.