Finite temperature effects in trapped Fermi gases with population imbalance

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 T0 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.” Recent work 1‐3 on trapped atomic Fermi gases with population imbalance has become particularly exciting. With the application of a magnetic field, these systems exhibit an evolution 4‐6 from BCS to Bose-Einstein condensation BEC. Not only are these gases possible prototypes for condensed matter systems 7,8 in the presence of a magnetic field and Zeeman coupling, but they may also be prototypes for particle and nuclear physics systems 9,10. These pioneering experiments have been done by two experimental groups 1,2. There are a number of key experimental observations which we now list. i Both groups have observed that the trap profiles are characterized by a central core of at most weakly polarized superfluid, surrounded 3 by a normal region where the bulk of the polarization is contained. ii The normal region appears to consist of overlapping clouds of both spin states “normal mixture”, followed at the edge of the cloud by a region consisting only of the majority component. These population imbalance experiments have been done 1,3 in conjunction with other measurements vortex excitations and magnetic field sweeps which establish the presence and the location for superfluid condensation. iii Even more recently 3 it has been demonstrated that the presence of superfluidity at and below Tc is directly reflected in changes in the shape of the clouds. iv Important for the present purposes is the fact that 3 there are strong interaction effects within the normal region of the cloud, which have not yet been incorporated in the theoretical literature 11,12. The goal of the present paper is to address the four points i‐iv listed above through a finite temperature theory of BCS-BEC crossover in the presence of population imbalance within a trap. A related study of the homogeneous system was presented earlier 13. What is unique to our work is the capability of separating in a natural way the condensed from noncondensed pair contributions to the trap profile; this is complicated by the fact that except at T=0 the presence of a fermionic excitation gap is not a signature of phase coherent superconductivity. We also present calculations of Tc in a trap and show how the general shape of the profile changes below and above Tc, unlike what is found experimentally and theoretically 14 in the absence of polarization. In a related fashion, we examine the noncondensed pair states in the trap and determine to what extent they differ from a free gas mixture of the two spin states. Our principal findings are at low T0 and for the unitary and near-BEC regimes: a the superfluid core seems to be robustly maintained at nearly zero polarization, and b the mixed normal region carries a significant fraction of the polarization within a nonsuperfluid state having strong pair correlations. Indeed, experiments suggest 3 that “even in the normal state, strong interactions significantly deform the density profile of the majority spin component.” Here we interpret these correlations as noncondensed pairs which have no counterpart at T=0 and which are associated with an excitation gap “pseudogap” in the fermionic spectrum. Finally, c in the course of making contact with points i‐iv listed above we show good qualitative agreement with the