Broken scale-invariance in time-dependent trapping potentials

TL;DR

This paper investigates how finite contact interactions break scale invariance in a cold atom gas under time-dependent harmonic confinement, affecting expansion dynamics and oscillation properties, with analytical and numerical insights.

Contribution

It demonstrates how finite interactions break scale invariance, altering expansion dynamics and oscillation behavior, contrasting with the scale-invariant Efimovian expansion.

Findings

Finiteness of interactions causes time-dependent oscillation periods and amplitudes.

Oscillation period approaches scale-invariant value at large times.

Analytical and numerical results support the impact of contact interactions.

Abstract

The response of a cold atom gas with contact interactions to a smoothly varying external harmonic confinement in the non-adiabatic regime is studied. The time variation of the angular frequency is varied such that the system is, for vanishing or infinitely strong contact interactions, scale invariant. The time evolution of the system with broken scale invariance (i.e., the time evolution of the system with finite interaction strength), is contrasted with that for a scale invariant system, which exhibits Efimovian-like expansion dynamics that is characterized by log-periodic oscillations with unique period and amplitude. It is found that the breaking of the scale invariance by the finiteness of the interactions leads to a time dependence of the oscillation period and amplitude. It is argued, based on analytical considerations for atomic gases of arbitrary size and numerical results for two one-dimensional particles, that the oscillation pe riod approaches that of the scale-invariant system at large times. The role of the time-dependent contact in the expansion dynamics is analyzed.