The important role of temperature in BCS--Bose-Einstein condensation crossover phenomena with population imbalance

Any comparison between theory and experiment in the cold Fermi gases requires that one include the effects of non-zero temperature $T$. In this talk we show how to include finite $T$ in a way which is compatible with the generalized BCS-like ground state, assumed in essentially all $T=0$ calculations of gases with population imbalance. We use a pairing fluctuation theory of BCS--Bose-Einstein condensation (BEC) based on a $T$-matrix formalism. Distinguishing this theory from strict mean-field theories is our self-consistent treatment of incoherent, finite-momentum pairs along with single fermions. This leads to a pseudogap in the fermion excitation spectrum at finite $T$ which is necessary in order to arrive at physically meaningful transition temperatures $T_c(p)$, where $p$ is the polarization. We present phase diagrams in the $p$-$T$ plane with variable scattering length, $1/k_Fa$, and identify the regions where bulk superfluidity, normal phases and phase separation appears. For the trapped Fermi gases, we present particle density profiles for general $1/k_Fa$ as well as a detailed comparison with recent measurements at both MIT and Rice University. We find reasonably good agreement with these experimental data. \\ 1. C.-C. Chien, Q.J. Chen, Y. He, and K. Levin, \textit{Intermediate temperature superfluidity in an atomic Fermi gas with population imbalance}, Phys. Rev. Lett. 97, 090402 (2006). \\ 2. Q.J. Chen, Y. He, C.-C. Chien, and K. Levin, \textit{Stability conditions and phase diagrams for two component Fermi gases with population imbalance}, cond-mat/0608454; Phys. Rev. A 74, 06xxxx (2006). \\ 3. C.-C. Chien, Q.J. Chen, Y. He, and K. Levin, \textit{Finite temperature effects in trapped Fermi gases with population imbalance}, Phys. Rev. A 74, 021602(R) 2006.