Superfluidity of fermion atoms loaded in a deep optical lattice: the existence of two rotonlike modes

TL;DR

This paper theoretically investigates collective excitations in fermionic superfluids in optical lattices, revealing two distinct rotonlike modes with different dispersions and critical flow momenta, which are experimentally observable.

Contribution

It introduces a comprehensive theoretical framework for analyzing collective modes in the attractive Hubbard model, identifying two novel rotonlike excitations with unique properties.

Findings

Two rotonlike modes with different dispersions are predicted.

Both modes are undamped and experimentally observable.

Critical flow momenta are identified for each rotonlike mode.

Abstract

We present theoretical calculations of collective modes of the one-band attractive Hubbard model which is widely used to study the s-wave superfluid phases of atomic Fermi gases of two-hyperfine states loaded in a deep optical lattice. To make our theory applicable for both superconductivity and superfluidity, we assume the more general $t-U-J$ Hamiltonian. Using the functional differentiation we derive Schwinger-Dyson equations for the single-particle Green's functions. The method of Legendre transform is used to give a systematic derivation of the Bethe-Salpeter (BS) equation for the two-particle Green's function and the associated collective modes. The numerical solution of the BS equation in the limit $J\rightarrow 0$ shows the existence of two rotonlike collective modes with different low-energy Goldstone dispersions and different positions of the rotonlike minima. The two rotonlike modes lie outside of the region determined by the lower boundary of the particle-hole continuum, and therefore, the two modes are not damped and they should be experimentally observable. In the presence of superfluid flow at a certain critical flow momentum, the minimum of the first rotonlike mode reaches zero energy, but this occurs before the minimum of the second mode and the lower boundary of the particle-hole continuum do, i.e. there are two critical flow momenta related to the existence of two rotonlike excitations.