Many-body interferometry of one-dimensional integrable systems

TL;DR

This paper introduces a method using many-body Ramsey interferometry to measure non-equilibrium correlation functions in 1D integrable systems, enabling distinction between GGE and thermal states with current ultracold atom technology.

Contribution

It proposes a novel experimental protocol for measuring response functions to differentiate post-quench phases in 1D integrable models, advancing non-equilibrium quantum dynamics studies.

Findings

Retarded Green's functions distinguish GGE from thermal states.

The protocol can be implemented with existing ultracold atom setups.

It enables studying non-thermal ensemble dynamics.

Abstract

We propose using many-body Ramsey interferometry to measure non-equilibrium correlation functions of one-dimensional (1D) integrable systems. The 1D transverse-field Ising model, which is conjectured to equilibrate into non-thermal Gibbs ensemble (GGE) steady states, is studied. It is shown that retarded Green's functions, as opposed to ordinary spin-spin correlators considered previously, can convincingly distinguish between the GGE and thermal post-quench steady states, justifying the assumption of convergence towards the GGE as the system equilibrates. We also propose the experimental protocol for measuring the response functions with Ramsey interferometry, which can be used to distinguish between different post-quench phases of the model. Our proposal can be realized with current ultracold atom techniques, and opens up the possibility to study dynamics in non-thermal ensembles.