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

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 counter-propagating
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.