Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap based quantum simulator

TL;DR

This paper investigates nonequilibrium retarded spin-spin Green's functions in a quantum simulator using a Ramsey protocol, deriving spectral moments, simulating dynamics, and applying compressive sensing to analyze correlation transport and excitation spectra.

Contribution

It extends previous work by analyzing nonequilibrium Green's functions in the transverse-field Ising model with a novel spectral analysis and efficient data extraction methods.

Findings

Short-time behavior relates to Lieb-Robinson bounds.

Long-time behavior reveals excitation spectra.

Compressive sensing enables efficient spectral analysis.

Abstract

Recent work proposed a variant on Ramsey interferometry for coupled spin-$1/2$ systems that directly measures the retarded spin-spin Green's function. We expand on that work by investigating nonequilibrium retarded spin-spin Green's functions within the transverse-field Ising model. We derive the lowest four spectral moments to understand the short-time behavior and we employ a Lehmann-like representation to determine the spectral behavior. We simulate a Ramsey protocol for a nonequilibrium quantum spin system that consists of a coherent superposition of the ground state and diabatically excited higher-energy states via a temporally ramped transverse magnetic field. We then apply the Ramsey spectroscopy protocol to the final Hamiltonian, which has a constant transverse field. The short-time behavior directly relates to Lieb-Robinson bounds for the transport of many-body correlations, while the long-time behavior relates to the excitation spectra of the Hamiltonian. Compressive sensing is employed in the data analysis to efficiently extract that spectra.