The $\mathcal{PT}$-symmetry-breaking transition in a chain of trapped interacting ions

TL;DR

This paper explores how interactions in a chain of trapped ions influence the $ ext{PT}$-symmetry-breaking transition, revealing that strong interactions can either enhance or suppress the transition depending on the chain length.

Contribution

It introduces the study of interaction effects on $ ext{PT}$-symmetry-breaking in ion chains, extending previous single-ion experiments to many-body systems.

Findings

Strong interactions can enhance the $ ext{PT}$-symmetric phase for even N.

Interactions can suppress the phase, making the system sensitive to infinitesimal dissipation.

Results are experimentally testable in ion chain setups.

Abstract

Trapped ions are an ideal platform to implement quantum simulation. Previously the parity-time reversal ($\mathcal{PT}$) symmetry-breaking transition in the paradigmatic non-Hermitian Hamiltonian $h_{PT}=J\sigma_x-i\Gamma\sigma_z$ has been observed in a single ion experiment in a passive way. In this work, we propose to study the interaction effects on the $\mathcal{PT}$-symmetry-breaking transition in a chain of $N$ trapped interacting ions. We consider an effective Ising interaction $H^\text{Ising-x}_\text{int} =\sum_{j<k}U_{jk}\sigma_x^j\sigma_x^k$ between the ions on top of $h_{PT}$. We find that sufficiently strong interaction strength can enhance the $\mathcal{PT}$-symmetric phase for even $N$ while the phase is suppressed in all the other cases. In particular, the suppression can be so strong that even infinitesimal dissipation, quantified by $\Gamma$, can turn the system into the $\mathcal{PT}$-symmetry-breaking phase. In addition, we assess the convolved effects due to the coupling and the spin phase shifts. Our findings can be readily tested in ion chain experiments.