Instability of superfluid Fermi gases induced by a roton-like density mode in optical lattices

TL;DR

This paper investigates the stability of superfluid Fermi gases in optical lattices, revealing a roton-like mode that causes instability at velocities below the pair-breaking threshold, especially across the BCS-BEC crossover.

Contribution

It introduces a detailed analysis of the roton-like excitations in superfluid Fermi gases within optical lattices and their role in superfluid instability.

Findings

Roton-like minimum appears in the AB mode spectrum due to charge-density-wave fluctuations.

Critical velocity for instability is lower than the pair-breaking velocity.

Superfluid instability is driven by roton emission, not pair-breaking.

Abstract

We study the stability of superfluid Fermi gases in deep optical lattices in the BCS--Bose-Einstein condensation (BEC) crossover at zero temperature. Within the tight-binding attractive Hubbard model, we calculate the spectrum of the low-energy Anderson-Bogoliubov (AB) mode as well as the single-particle excitations in the presence of superfluid flow in order to determine the critical velocities. To obtain the spectrum of the AB mode, we calculate the density response function in the generalized random-phase approximation applying the Green's function formalism developed by C\^ot\'e and Griffin to the Hubbard model. We find that the spectrum of the AB mode is separated from the particle-hole continuum having the characteristic rotonlike minimum at short wavelength due to the strong charge-density-wave fluctuations. The energy of the rotonlike minimum decreases with increasing the lattice velocity and it reaches zero at the critical velocity which is smaller than the pair breaking velocity. This indicates that the superfluid state is energetically unstable due to the spontaneous emission of the short-wavelength rotonlike excitations of the AB mode instead due to pair-breaking. We determine the critical velocities as functions of the interaction strength across the BCS-BEC crossover regime.