Collective modes and the speed of sound in the Fulde-Ferrell-Larkin-Ovchinnikov state

Abstract

We consider the density response of a spin-imbalanced ultracold Fermi gas in an optical lattice in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We calculate the collective mode spectrum of the system in the generalised random phase approximation and find that though the collective modes are damped even at zero tempererature, the damping is weak enough to have well-defined collective modes. We calculate the speed of sound in the gas and show that it is anisotropic due to the anisotropy of the FFLO pairing, which implies an experimental signature for the FFLO state.

The Fulde–Ferrell–Larkin–Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review

“…The existence of quasiparticles, even at low energy, is due to the gapless nature of the FF state, however in higher dimensions, they are more dispersed and do not form a stripe. The results of [131] differ at higher momenta from those in [136,137]: there is no gapless sound mode around k * = 2(k F ↑ − k F ↓ ) because in the FF case, |∆| is constant and the excess fermions are uniformely distributed. The backbending of the collective mode dispersion in 2D and 3D lattices at large momenta has also been interpreted as a rotonlike behaviour [142,143,144,145].…”

“…Radzihovsky [109,146] derived a low-energy Landau theory for the LO state in a two-component Fermi gas and found two Goldstone modes, one corresponding to superfluidity and one that he refers Figure 16. The dispersion relation of the collective density modes in the FFLO state in a 2D lattice, from [131]. The wave vector is parallel to the the FFLO vector q in the x-direction (ωx), and perpendicular to it in y (ωy).…”

Collective Modes of a Soliton Train in a Fermi Superfluid

“…Past studies on FFLO have focused on the phase that minimizes the free energy, which occurs at specific values of k 0 within a limited region of the phase diagram [51,52]. Low-energy collective excitations of energetically stable FFLO states have been explored using different theoretical techniques [45][46][47]62], and methods for detecting such states have been proposed [44]. However, we find that a C-FFLO phase is always dynamically stable, even when there are lower-energy states available.…”

“…Using phase-imprinting techniques [14,26,27,42], one can generate a train of solitons in the superfluid. The collective modes of the soli-ton train would show up as pronounced peaks in spectroscopic measurements of the pairing susceptibility, or in the density response of the system [43][44][45][46][47]. Here we extract the collective modes by linearizing the selfconsistent Bogoliubov-de Gennes (BdG) equations governing the fermion fields.…”

Bound collective modes in nonuniform superconductors

“…[43] It is then plausible that in some frequency range, depending on the availability of excitation phase space, the collective modes near a domain wall will not be overdamped. [44] The complete treatment of dynamics of coupled order parameter modes, excitations and charge density will require future fully microscopic calculation.…”