The $\mathcal{PT}$-symmetry-breaking transition in a chain of trapped interacting ions
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| Format: | Preprint |
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2024
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| _version_ | 1866913564807135232 |
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| author | Hu, Zhenxin Yu, Zhenhua |
| author_facet | Hu, Zhenxin Yu, Zhenhua |
| contents | 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 $h_{PT}=Jσ_x-iΓσ_z$ 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 $H^\text{Ising-x}_\text{int} =\sum_{j<k}U_{jk}σ_x^jσ_x^k$ 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 $Γ$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20091 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $\mathcal{PT}$-symmetry-breaking transition in a chain of trapped interacting ions Hu, Zhenxin Yu, Zhenhua Quantum Gases 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 $h_{PT}=Jσ_x-iΓσ_z$ 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 $H^\text{Ising-x}_\text{int} =\sum_{j<k}U_{jk}σ_x^jσ_x^k$ 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 $Γ$, 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. |
| title | The $\mathcal{PT}$-symmetry-breaking transition in a chain of trapped interacting ions |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2410.20091 |