Separation of Timescales in a Quantum Newton's Cradle

TL;DR

This paper models the dynamics of strongly repulsive bosons in one dimension after a Bragg pulse, revealing a separation of rapid and slow timescales in their relaxation and periodic behavior.

Contribution

It provides an exact theoretical analysis of post-pulse dynamics in Lieb-Liniger gases using Fermi-Bose mapping and Quench Action methods.

Findings

Clear separation of rapid and slow relaxation timescales

Exact reconstruction of many-body time evolution

Observation of in-trap periodic behavior

Abstract

For strongly repulsive bosons in one dimension, we provide detailed modeling of the Bragg pulse used in quantum Newton's cradle-like settings or in Bragg spectroscopy experiments. By employing the Fermi-Bose mapping for a finite harmonically trapped gas and the Quench Action approach for a thermodynamic system on a ring, we reconstruct the exact post-pulse many-body time evolution of Lieb-Liniger gases in the Tonks-Girardeau limit, together with their changing local density profile and momentum distribution. Our results display a clear separation of timescales between rapid and trap-insensitive relaxation immediately after the pulse, followed by slow in-trap periodic behaviour.