Nonequilibrium Damping of Collective Motion of Homogeneous Cold Fermi Condensates with Feshbach Resonances

TL;DR

This paper investigates the collisionless damping of collective modes in cold Fermi condensates with Feshbach resonances across BCS and BEC regimes, revealing how resonance width influences decay behavior and phase-amplitude interactions.

Contribution

It provides a detailed analysis of damping behaviors for broad and narrow Feshbach resonances, highlighting the universal decay in the narrow case and phase effects on amplitude saturation.

Findings

Amplitude decays as t^{-1/2} in BCS for broad resonance

Amplitude decays as t^{-3/2} in BEC for broad resonance

Narrow resonance exhibits t^{-3/2} decay across regimes

Abstract

Collisionless damping of a condensate of cold Fermi atoms, whose scattering is controlled by a Feshbach resonance, is explored throughout the BCS and BEC regimes when small perturbations on its phase and amplitude modes are turned on to drive the system slightly out of equilibrium. Using a one-loop effective action, we first recreate the known result that for a broad resonance the amplitude of the condensate decays as $t^{-1/2}$ at late times in the BCS regime whereas it decays as $t^{-3/2}$ in the BEC regime. We then examine the case of an idealized narrow resonance, and find that this collective mode decays as $t^{-3/2}$ throughout both the BCS and BEC regimes. Although this seems to contradict earlier results that damping is identical for both broad and narrow resonances, the breakdown of the narrow resonance limit restores this universal behaviour. More measureably, the phase perturbation may give a shift on the saturated value to which the collective amplitude mode decays, which vanishes only in the deep BCS regime when the phase and amplitude modes are decoupled.