# Dynamically generated correlations in a trapped bosonic gas via frequency quenches

## TL;DR

This paper investigates how stochastic frequency quenches in a trapped bosonic gas induce nontrivial correlations and a nonequilibrium steady state, revealing universal scaling laws and complex statistical structures.

## Contribution

It introduces a novel protocol of repeated quantum quenches that drives a bosonic gas into a unique NESS with emergent long-range correlations and provides analytical and numerical characterization of this state.

## Key findings

- Discovery of a CIID structure in the joint probability density function
- Identification of long-range dynamical correlations in the NESS
- Universal scaling laws in order and gap statistics

## Abstract

We study a system of $N$ noninteracting bosons in a harmonic trap subjected to repeated quantum quenches, where the trap frequency is switched from one value to another after a random time duration drawn from an exponential distribution. Each cycle contains two steps: (i) changing the trap frequency to enable unitary evolution under a Hamiltonian, and (ii) reapplying the original trap at stochastic times to cool the gas back to its initial state. This protocol effectively makes it an open quantum system and drives it into a unique nonequilibrium steady state (NESS). We analytically and numerically characterize the NESS, uncovering a conditionally independent and identically distributed (CIID) structure in the joint probability density function (JPDF) of the positions. The JPDF in the CIID structure is a product of Gaussians with a common random variance, which is then averaged with respect to its distribution, making the JPDF non-factorizable, giving rise to long-range emergent dynamical correlations. The average density profile of the gas shows significant deviations from the initial Gaussian shape. We further compute the order and the gap statistics, revealing universal scaling in both bulk and edge regimes. We also analyze the full counting statistics, exposing rich parameter-dependent structure. Our results demonstrate how stochastic quenches can generate nontrivial correlations in quantum many-body systems.