# Realizing Fulde-Ferrell Superfluids via a Dark-State Control of Feshbach Resonances

## TL;DR

This paper proposes a method to realize Fulde-Ferrell superfluidity in ultracold Fermi gases by optically controlling Feshbach resonances, predicting unique anisotropic properties and experimental signatures.

## Contribution

It introduces a novel optical dark-state scheme to induce Fulde-Ferrell superfluidity with nonzero momentum pairing in ultracold gases.

## Key findings

- Fulde-Ferrell state exhibits anisotropic dispersion
- Suppressed superfluid density at zero temperature
- Anisotropic sound velocity and rotonic modes

## Abstract

We propose that the long-sought Fulde-Ferrell superfluidity with nonzero momentum pairing can be realized in ultracold two-component Fermi gases of $^{40}$K or $^{6}$Li atoms by optically tuning their magnetic Feshbach resonances via the creation of a closed-channel dark state with a Doppler-shifted Stark effect. In this scheme, two counterpropagating optical fields are applied to couple two molecular states in the closed channel to an excited molecular state, leading to a significant violation of Galilean invariance in the dark-state regime and hence to the possibility of Fulde-Ferrell superfluidity. We develop a field theoretical formulation for both two-body and many-body problems and predict that the Fulde-Ferrell state has remarkable properties, such as anisotropic single-particle dispersion relation, suppressed superfluid density at zero temperature, anisotropic sound velocity and rotonic collective mode. The latter two features can be experimentally probed using Bragg spectroscopy, providing a smoking-gun proof of Fulde-Ferrell superfluidity.