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 (24)

• Many-Body Physics with Ultracold Gases
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Transport and conservation laws
• Universal Spin Transport in a Strongly Interacting Fermi Gas
• Collective oscillations of a 1D trapped Bose gas
• A Mixture of Bose and Fermi Superfluids
• Breathing Modes and Hidden Symmetry of Trapped Atoms in 2D
• Observation of spin Coulomb drag in a two-dimensional electron gas
• Scale invariance and viscosity of a two-dimensional Fermi gas
• Transport in Almost Integrable Models: Perturbed Heisenberg Chains
• Memory matrix theory of magnetotransport in strange metals
• Transport near the Ising-nematic quantum critical point of metals in two dimensions
• An Example of Quantum Anomaly in the Physics of Ultra-Cold Gases
• Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas
• Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder
• Diffusion equation and spin drag in spin-polarized transport
• 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
• Breakdown of scale invariance in a quasi-two-dimensional Bose gas due to the presence of the third dimension
• Dipole Oscillations in Fermionic Mixtures
• Breakdown of the scale invariance in the vicinity of Tonks-Girardeau gas

Cited by in corpus (7)

• Universal Spin Transport and Quantum Bounds for Unitary Fermions
• Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases
• Scale and conformal invariance in rotating interacting few-fermion systems
• Spin Hall mode in a trapped thermal Rashba gas
• Decay of the Kohn mode in hydrodynamic regime
• Thermalization of dipole oscillations in confined systems by rare collisions
• Drag dynamics in one-dimensional Fermi systems