Aspects of Superfluid Cold Atomic Gases in Optical Lattices

TL;DR

This paper reviews the properties and behaviors of superfluid Bose and Fermi gases in optical lattices, focusing on their static, dynamic, and band structure characteristics, especially near the BCS-BEC crossover.

Contribution

It provides a unified analysis of superfluid Fermi and Bose gases in optical lattices, highlighting the emergence of swallowtail band structures and stability considerations.

Findings

Swallowtail band structures can form in superfluid Fermi gases.

Strong atom pairing affects static properties and superflow stability.

Different mechanisms lead to swallowtail formation in Fermi and Bose gases.

Abstract

We review our studies on Bose and Fermi superfluids of cold atomic gases in optical lattices at zero temperature. Especially, we focus on superfluid Fermi gases along the crossover between the Bardeen-Cooper-Schrieffer (BCS) and the Bose-Einstein condensate (BEC) states, which enable us to study the Bose and the Fermi superfluids in a unified point of view. We discuss basic static and long-wavelength properties (such as the equation of state, incompressibility, and effective mass), energetic stability, and energy band structures of the superfluid Fermi gases in an optical lattice periodic along one spatial direction. The periodic potential causes pairs of atoms to be strongly bound, and this can affect the static and long-wavelength properties and the stability of the superflow. Regarding the band structure, a peculiar loop structure called "swallowtail" can appear in superfluid Fermi gases and in the Bose case, but the mechanism of emergence in the Fermi case is very different from that in bosonic case. Other quantum phases that the cold atomic gases in optical lattices can show are also briefly discussed based on their roles as quantum simulators of Hubbard models.