Equilibrium and off-equilibrium trap-size scaling in 1D ultracold bosonic gases

TL;DR

This paper investigates the universal scaling behavior of one-dimensional ultracold bosonic gases under varying trap sizes, analyzing both equilibrium and non-equilibrium dynamics using analytical and numerical methods.

Contribution

It introduces a universal trap-size scaling framework for 1D bosonic gases, applicable to both continuum and lattice models, during equilibrium and dynamic evolution.

Findings

Universal power-law trap-size scaling laws identified.

Scaling functions for key observables computed.

Results applicable to cold atomic gas experiments.

Abstract

We study some aspects of equilibrium and off equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles N and study their scaling behavior with increasing the trap size. We focus on one-dimensional (1D) bosonic systems, such as gases described by the Lieb-Liniger model and its Tonks-Girardeau limit of impenetrable bosons, and gases constrained in optical lattices as described by the Bose-Hubbard model. We study their quantum (zero-temperature) behavior at equilibrium and off equilibrium during the unitary time evolution arising from changes of the trapping potential, which may be instantaneous or described by a power-law time dependence, starting from the equilibrium ground state for a initial trap size. Renormalization-group scaling arguments, analytical and numerical calculations show that the trap-size dependence of the equilibrium and off-equilibrium dynamics can be cast in the form of a trap-size scaling in the low-density regime, characterized by universal power laws of the trap size, in dilute gases with repulsive contact interactions and lattice systems described by the Bose-Hubbard model. The scaling functions corresponding to several physically interesting observables are computed. Our results are of experimental relevance for systems of cold atomic gases trapped by tunable confining potentials.