Equilibration and Approximate Conservation Laws: Dipole Oscillations and Perfect Drag of Ultracold Atoms in a Harmonic Trap

TL;DR

This paper explores how approximate conservation laws affect the relaxation of dipole oscillations in ultracold fermionic atoms trapped in a harmonic potential, revealing conditions for perfect drag and slow damping.

Contribution

It introduces a detailed analysis of dipole oscillation relaxation using memory-matrix methods, highlighting the role of dynamical symmetry breaking and interaction strength in ultracold atom systems.

Findings

Near-perfect drag occurs when interactions dominate.

Small frequency detuning breaks symmetry and causes damping.

Decay rate scales as $( ext{detuning})^2 / ext{scattering rate}$.

Abstract

The presence of (approximate) conservation laws can prohibit the fast relaxation of interacting many-particle quantum systems. We investigate this physics by studying the center-of-mass oscillations of two species of fermionic ultracold atoms in a harmonic trap. If their trap frequencies are equal, a dynamical symmetry (spectrum generating algebra), closely related to Kohn's theorem, prohibits the relaxation of center-of-mass oscillations. A small detuning $\delta\omega$ of the trap frequencies for the two species breaks the dynamical symmetry and ultimately leads to a damping of dipole oscillations driven by inter-species interactions. Using memory-matrix methods, we calculate the relaxation as a function of frequency difference, particle number, temperature, and strength of inter-species interactions. When interactions dominate, there is almost perfect drag between the two species and the dynamical symmetry is approximately restored. The drag can either arise from Hartree potentials or from friction. In the latter case (hydrodynamic limit), the center-of-mass oscillations decay with a tiny rate, $1/\tau \propto (\delta\omega)^2/\Gamma$, where $\Gamma$ is a single particle scattering rate.