Abstract
Atomic Fermi gases have been an ideal platform for simulating conventional and engineering exotic physical systems owing to their multiple tunable control parameters. Here we investigate the effects of mixed dimensionality on the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas with a short-range pairing interaction, while one component is confined on a one-dimensional (1D) optical lattice whereas the other is in a homogeneous 3D continuum. We study the phase diagram and the pseudogap phenomena throughout the entire BCS-BEC crossover, using a pairing fluctuation theory. We find that the effective dimensionality of the non-interacting lattice component can evolve from quasi-3D to quasi-1D, leading to strong Fermi surface mismatch. Upon pairing, the system becomes effectively quasi-two dimensional in the BEC regime. The behavior of Tc bears similarity to that of a regular 3D population imbalanced Fermi gas, but with a more drastic departure from the regular 3D balanced case, featuring both intermediate temperature superfluidity and possible pair density wave ground state. Unlike a simple 1D optical lattice case, Tc in the mixed dimensions has a constant BEC asymptote.
Highlights
Ultracold atomic gases have been under active investigation in the past decades with their remarkable tunability in terms of interaction, population and mass imbalance[1,2], and so on
Deviation from these parameters lead to drastic Fermi surface mismatch, and the resulting phase diagrams can become quite different from their counterpart of the polarized Fermi gases in regular 3D continuum
Before we present our solutions on the phase diagrams, let’s first study the Fermi surface mismatch in the noninteracting limit
Summary
We use the same formalism as given in ref.[15], which is adapted for the mixed dimensions. K = ( k↑ + k↓)/2, with kσ = ξkσ + μσ Note that this scattering length in necessarily different from that defined in ordinary 3D or 2D continuum, and is relevant to the actual scattering length in the presence of the optical lattice, via, e.g., the binding energy εB = 2/2mra[2] in the BEC regime. In this way, the divergance of the scattering length a corresponds to the threshold interaction strength gc for two fermions to form a zero binding energy bound state in the mixed dimensions, and where the actual s-wave scattering phase shift is π/2, i.e., the unitary scattering. Phase separation may occur when this stability condition is not satisfied
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