Superfluidity and BCS-BEC crossover of ultracold atomic Fermi gases in mixed dimensions

Atomic Fermi gases have been under active investigation in the past decade. Here we study the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas in the presence of mixed dimensionality, in which one component is confined on a 1D optical lattice whereas the other is free in the 3D continuum. We assume a short-range pairing interaction and determine the superfluid transition temperature $T_c$ and the phase diagram for the entire BCS-BEC crossover, using a pairing fluctuation theory which includes self-consistently the contributions of finite momentum pairs. We find that, as the lattice depth increases and the lattice spacing decreases, the behavior of $T_c$ becomes very similar to that of a population imbalance Fermi gas in a simple 3D continuum. There is no superfluidity even at $T=0$ below certain threshold of pairing strength in the BCS regime. Nonmonotonic $T_c$ behavior and intermediate temperature superfluidity emerge, and for deep enough lattice, the $T_c$ curve will split into two parts. Implications for experiment will be discussed. References: 1. Q.J. Chen, Ioan Kosztin, B. Janko, and K. Levin, Phys. Rev. B 59, 7083 (1999). 2. Chih-Chun Chien, Qijin Chen, Yan He, and K. Levin, Phys. Rev. Lett. 97, 090402(2006).