# Quantum Work of an Optical Lattice

## TL;DR

This paper investigates the global non-equilibrium behavior of a Lieb-Liniger gas released from an optical lattice by calculating the work distribution, revealing universal properties, interaction effects, and the role of bound states.

## Contribution

It provides a Bethe Ansatz-based analysis of the work distribution and Loschmidt amplitude for the Lieb-Liniger gas post-quench, including attractive interactions and bound state effects.

## Key findings

- Universal edge exponents in work distribution
- Interaction-dependent decay of Loschmidt echo
- Bound states enable work extraction with low probability

## Abstract

A classic example of a quantum quench concerns the release of a interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied however the global properties of these non-equilibrium quantum systems have received far less attention. Here we study several aspects of global non-equilibrium behavior by calculating the amount of work done by the quench as measured through the work distribution function. Using Bethe Ansatz techniques we determine the Loschmidt amplitude and work distribution function of the Lieb-Liniger gas after it is released from an optical lattice. We find the average work and its universal edge exponents from which we determine the long time decay of the Loshcmidt echo and highlight striking differences caused by the the interactions as well as changes in the geometry of the system. We extend our calculation to the attractive regime of the model and show that the system exhibits properties similar to the super Tonks-Girardaeu gas. Finally we examine the prominent role played by bound states in the work distribution and show that, with low probability, they allow for work to be extracted from the quench.