Relaxation of Fermionic Excitations in a Strongly Attractive Fermi Gas in an Optical Lattice

TL;DR

This paper theoretically investigates how high-energy fermionic excitations relax into molecules in an attractive Fermi gas within an optical lattice, revealing the dependence of relaxation rates on interaction strength, temperature, and filling.

Contribution

It provides explicit formulas for relaxation rates in different phases and demonstrates the decoupling of quasiparticle and phase degrees of freedom, enabling observation of ordered states at high energies.

Findings

Relaxation rate scales as ~ Ct exp(-α U^2/t^2) in large U/t limit.

Relaxation rate decreases with increasing temperature and deviation from half-filling.

Quasiparticle and phase degrees of freedom are effectively decoupled within experimental timescales.

Abstract

We theoretically study the relaxation of high energy single particle excitations into molecules in a system of attractive fermions in an optical lattice, both in the superfluid and the normal phase. In a system characterized by an interaction scale $U$ and a tunneling rate $t$, we show that the relaxation rate scales as $\sim Ct\exp(-\alpha U^2/t^2)$ in the large $U/t$ limit. We obtain explicit expressions for the exponent $\alpha$, both in the low temperature superfluid phase and the high temperature phase with pairing but no coherence between the molecules. We find that the relaxation rate decreases both with temperature and deviation of the fermion density from half-filling. We show that quasiparticle and phase degrees of freedom are effectively decoupled within experimental timescales allowing for observation of ordered states even at high total energy of the system.