# Probing non-thermal density fluctuations in the one-dimensional Bose gas

## TL;DR

This paper presents a method to experimentally determine the non-thermal density fluctuations in a one-dimensional Bose gas by analyzing the dynamical structure factor after a quantum quench, using a generalized fluctuation-dissipation theorem.

## Contribution

It introduces a novel approach to reconstruct the generalized Gibbs ensemble of an integrable quantum system from experimental data.

## Key findings

- Reconstruction of the stationary state from dynamical measurements.
- Validation of a generalized fluctuation-dissipation relation.
- Feasibility of experimental measurement of multiple effective temperatures.

## Abstract

Quantum integrable models display a rich variety of non-thermal excited states with unusual properties. The most common way to probe them is by performing a quantum quench, i.e., by letting a many-body initial state unitarily evolve with an integrable Hamiltonian. At late times, these systems are locally described by a generalized Gibbs ensemble with as many effective temperatures as their local conserved quantities. The experimental measurement of this macroscopic number of temperatures remains elusive. Here we show that they can be obtained by probing the dynamical structure factor of the system after the quench and by employing a generalized fluctuation-dissipation theorem that we provide. Our procedure allows us to completely reconstruct the stationary state of a quantum integrable system from state-of-the-art experimental observations.