Relaxation of Bosons in One Dimension and the Onset of Dimensional Crossover

TL;DR

This study investigates the relaxation dynamics of ultra-cold bosons in a 1D setting, revealing a two-stage process involving rapid dephasing and slow thermalization, and explores the dimensional crossover from 1D to 3D.

Contribution

It provides experimental insights into the relaxation mechanisms and the breaking of integrability in 1D bosonic systems during the dimensional crossover.

Findings

Observation of a two-stage relaxation process.

Quantitative agreement with semiclassical simulations.

Control of dynamics through initial momentum imprints.

Abstract

We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.