Pure pairing modes in trapped fermion systems

Abstract

We present numerical predictions for the shape of the pairing fluctuations in harmonically trapped atomic 6Li with two spin projections, based on the fluiddynamical description of cold fermions with pairing interactions. In previous works it has been shown that when the equilibrium of a symmetric mixture is perturbed, the linearized fluiddynamic equations decouple into two sets, one containing the sound mode of fermion superfluids and the other the pairing mode. The latter corresponds to oscillations of the modulus of the complex gap and is driven by the kinetic energy densities of the particles and of the pairs. Assuming proportionality between the heat flux and the energy gradient, the particle kinetic energy undergoes a diffusive behavior and the diffusion parameter is the key parameter for the relaxation time scale. We examine a possible range of values for this parameter and find that the shape of the pairing oscillation is rather insensitive to the precise value of the transport coefficient. Moreover, the pairing fluctuation is largely confined to the center of the trap, and the energy of the pairing mode is consistent with the magnitude of the equilibrium gap.