Probing real-space and time resolved correlation functions with many-body Ramsey interferometry

TL;DR

This paper proposes a method using Ramsey interferometry with single-site addressability in synthetic matter to measure real-space and time resolved spin correlation functions, aiding in characterizing many-body states and phase transitions.

Contribution

It introduces a novel technique combining Ramsey interferometry and single-site addressability to directly measure dynamic correlation functions in quantum many-body systems.

Findings

The method can characterize excitations and phase transitions.

Spin-echo protocol mitigates experimental imperfections.

Application examples include 2D Heisenberg and 1D long-range Ising models.

Abstract

We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.