Observation of Non-Markovian Spin Dynamics in a Jaynes-Cummings-Hubbard Model using a Trapped-Ion Quantum Simulator

TL;DR

This paper demonstrates the use of a trapped-ion quantum simulator to explore non-Markovian spin dynamics in the Jaynes-Cummings-Hubbard model with up to 32 ions, revealing complex many-body and open quantum system behaviors.

Contribution

It is the first to simulate the JCH model with up to 32 ions, extending the effective Hilbert space and analyzing non-Markovian dynamics in a controllable quantum system.

Findings

Verified simulation results for large ion numbers

Extended to 32 excitations with an effective dimension of 2^77

Explored the dependence of non-Markovian dynamics on Hilbert space size

Abstract

Jaynes-Cummings-Hubbard (JCH) model is a fundamental many-body model for light-matter interaction. As a leading platform for quantum simulation, the trapped ion system has realized the JCH model for two to three ions. Here we report the quantum simulation of the JCH model using up to 32 ions. We verify the simulation results even for large ion numbers by engineering low excitations and thus low effective dimensions; then we extend to 32 excitations for an effective dimension of $2^{77}$, which is difficult for classical computers. By regarding the phonon modes as baths, we explore Markovian or non-Markovian spin dynamics in different parameter regimes of the JCH model, similar to quantum emitters in a structured photonic environment. We further examine the dependence of the non-Markovian dynamics on the effective Hilbert space dimension. Our work demonstrates the trapped ion system as a powerful quantum simulator for many-body physics and open quantum systems.