Collective excitations of superfluid Fermi gases near the transition temperature

Abstract

Studying the collective pairing phenomena in a two-component Fermi gas, we predict the appearance near the transition temperature ${T}_{c}$ of a well-resolved collective mode of quadratic dispersion. The mode is visible both above and below ${T}_{c}$ in the system's response to a driving pairing field. When approaching ${T}_{c}$ from below, the phononic and pair-breaking branches, characteristic of the zero temperature behavior, reduce to a relatively low energy-momentum region. Elsewhere they are replaced by the quadratically dispersed pairing resonance, which thus acts as a precursor of the phase transition. In the strong-coupling and Bose-Einstein condensate regime, this mode is a weakly damped propagating mode associated with a Lorentzian resonance. Conversely, in the BCS limit it is a relaxation mode of pure imaginary eigenenergy. At large momenta, the resonance disappears when it is reabsorbed by the lower edge of the pairing continuum. At intermediate temperatures between 0 and ${T}_{c}$ we unify the newly found collective phenomena near ${T}_{c}$ with the phononic and pair-breaking branches predicted from previous studies, and we exhaustively classify the roots of the analytically continued dispersion equation, and show that they provided a very good summary of the pair spectral functions.