Probing Polariton Dynamics in Trapped Ions with Phase-Coherent Two-Dimensional Spectroscopy

TL;DR

This paper introduces a phase-coherent three-pulse spectroscopy method to study polariton dynamics in trapped ions, enabling phase-sensitive analysis of many-excitation states and phase transitions.

Contribution

It presents a novel spectroscopy scheme that probes excitation-preserving dynamics in trapped-ion systems, revealing phase transitions and decoherence effects.

Findings

Two-dimensional spectra distinguish superfluid and insulator phases.

The method identifies decoherence mechanisms through lineshape analysis.

Numerical simulations validate the spectroscopy's effectiveness.

Abstract

We devise a phase-coherent three-pulse protocol to probe the polariton dynamics in a trapped-ion quantum simulation. In contrast to conventional nonlinear signals, the presented scheme does not change the number of excitations in the system, allowing for the investigation of the dynamics within an $N$-excitation manifold. In the particular case of a filling factor one ($N$ excitations in an $N$-ion chain), the proposed interaction induces coherent transitions between a delocalized phonon superfluid and a localized atomic insulator phase. Numerical simulations of a two-ion chain demonstrate that the resulting two-dimensional spectra allow for the unambiguous identification of the distinct phases, and the two-dimensional lineshapes efficiently characterize the relevant decoherence mechanism.