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

Abstract

Trapped ions are an ideal platform to implement quantum simulation. Previously the parity-time reversal ($\mathcal{P}\mathcal{T}$) 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 $\mathcal{P}\mathcal{T}$-symmetry-breaking transition in a chain of $N$ trapped interacting ions. We consider an effective Ising interaction $H_{\text{int}}^{\text{Ising-x}}={\sum }_{j<k}{U}_{jk}{\sigma }_x^j{\sigma }_x^k$ between the ions on top of $h_{PT}$. We find that sufficiently strong interaction strength can enhance the $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-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.

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Observation of parity-time symmetry breaking in a single spin system
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Non-Hermitian dynamics and $\mathcal{P}\mathcal{T}$-symmetry breaking in interacting mesoscopic Rydberg platforms
• Interacting non-Hermitian ultracold atoms in a harmonic trap: Two-body exact solution and high-order exceptional point
• Interaction effects on $\mathcal{P}\mathcal{T}$-symmetry breaking transition in atomic gases
• Super-exponential diffusion in nonlinear non-Hermitian systems