On a scale-invariant Fermi gas in a time-dependent harmonic potential

Abstract

We investigate a scale-invariant two-component Fermi gas in a time-dependent isotropic harmonic potential. The exact time evolution of the density distribution in position space in any spatial dimension is obtained. Two experimentally relevant examples, an abrupt change and a periodic modulation of the trapping frequency are solved. Small deviations from scale invariance and isotropy of the confinement are addressed within first order perturbation theory. We discuss the consequences for experiments with ultracold quantum gases such as the excitation of a tower of undamped breathing modes and a new alternative for measuring the Tan contact.

6+3 pages, 2 figures; revised and extended version

References in corpus (6)

• Theory of ultracold Fermi gases
• Nonrelativistic conformal field theories
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Scale invariance and viscosity of a two-dimensional Fermi gas
• Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas
• Occupation numbers of the harmonically trapped few-boson system

Cited by in corpus (19)

• General relations for quantum gases in two and three dimensions. Two-component fermions
• Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
• Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
• Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps
• Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations
• Two Cold Atoms in a Time-Dependent Harmonic Trap in One Dimension
• Simulation of Time-dependent Heisenberg Models in 1D
• Harmonically trapped Fermi gas: Temperature dependence of the Tan contact
• Collective modes of ultracold fermionic alkaline-earth gases with SU(N) symmetry
• Broken scale-invariance in time-dependent trapping potentials
• Non-Perturbative Dynamical Effects in Nearly Scale Invariant Systems: The Action of Breaking Scale Invariance
• Dynamics of strongly interacting Fermi gases with time-dependent interactions: Consequence of conformal symmetry
• Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases
• Complex scaling flows in the quench dynamics of interacting particles
• Higher-Harmonic Collective Modes in a Trapped Gas from Second-Order Hydrodynamics
• Emergent Infrared Conformal Dynamics in Strongly Interacting Quantum Gases
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Scale and conformal invariance in rotating interacting few-fermion systems
• Strongly Interacting Fermi Gases: Hydrodynamics and Beyond