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

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.

9 pages + 5 pages of appendix, 9 figures; changes in v2: updated citations

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Memory matrix theory of magnetotransport in strange metals
• Spin conductivity in almost integrable spin chains
• Apparent low-energy scale invariance in two-dimensional Fermi gases
• Spin Drag and Spin-Charge Separation in Cold Fermi Gases
• Collisional Properties of a Polarized Fermi Gas with Resonant Interactions
• Lower bounds for the conductivities of correlated quantum systems

Cited by in corpus (2)

• Spin Hall mode in a trapped thermal Rashba gas
• Decay of the Kohn mode in hydrodynamic regime