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arXiv:2006.16467 · Physical Review A

Observation of PT -symmetric quantum coherence in a single-ion system

Weichen Wang, Yan‐Li Zhou, Hui-Lai Zhang, Jie Zhang, Man-Chao Zhang, Yi Xie, Chun-Wang Wu, Ting Chen, Bao-Quan Ou, Wei Wu, Hui Jing, Ping‐Xing Chen

Published Feb 15, 2021• 83 citations
arXivHTMLPDF

Abstract

Parity-time ($\mathcal{PT}$)-symmetric systems, featuring real eigenvalues despite their non-Hermitian nature, undergo spontaneous $\mathcal{PT}$ symmetry breaking at the exceptional point (EP). The phase transition from $\mathcal{PT}$ symmetry to $\mathcal{PT}$ symmetry breaking has shown exotic functionalities in the classical realm, such as loss-induced transparency or lasing revival. This transition is also expected to produce a more unconventional effect in pure quantum $\mathcal{PT}$ devices. Here, we report experimental evidences of spontaneous $\mathcal{PT}$ symmetry breaking in a single cold $^{40}\mathrm{Ca}^{+}$ ion and, more importantly, a counterintuitive effect of perfect quantum coherence occurring at the EP. Excellent agreement between experimental results and theoretical predictions is identified. In view of the versatile role of cold ions in building a quantum memory or processor, our experiment provides an alternative platform to explore $\mathcal{PT}$-symmetric physics and utilize pure quantum EP effects.

DOI
10.1103/physreva.103.l020201

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Trapped ions are an ideal platform to implement quantum simulation. Previously, the parity-time ($\mathcal{PT}$)-reversal symmetry-breaking transition in the paradigmatic non-Hermitian Hamiltonian ${h}_{\mathcal{PT}}=J{\ensuremath{\sigma}}_{x}\ensuremath{-}i\mathrm{\ensuremath{\Gamma}}{\ensuremath{\sigma}}_{z}$ was 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 ${H}_{\text{int}}^{\text{Ising}\phantom{\rule{4.pt}{0ex}}x}={\ensuremath{\sum}}_{j<k}{U}_{jk}{\ensuremath{\sigma}}_{x}^{j}{\ensuremath{\sigma}}_{x}^{k}$ between the ions on top of ${h}_{\mathcal{PT}}$. 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 $\mathrm{\ensuremath{\Gamma}}$, 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.

arXiv:2410.20091•Physical Review A•Oct 2, 2024•0 citations
Parity-time (PT\mathcal{PT}PT)-symmetric systems, featuring real eigenvalues despite their non-Hermitian nature, undergo spontaneous PT\mathcal{PT}PT symmetry breaking at the exceptional point (EP). The phase transition from PT\mathcal{PT}PT symmetry to PT\mathcal{PT}PT symmetry breaking has shown exotic functionalities in the classical realm, such as loss-induced transparency or lasing revival. This transition is also expected to produce a more unconventional effect in pure quantum PT\mathcal{PT}PT devices. Here, we report experimental evidences of spontaneous PT\mathcal{PT}PT symmetry breaking in a single cold 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion and, more importantly, a counterintuitive effect of perfect quantum coherence occurring at the EP. Excellent agreement between experimental results and theoretical predictions is identified. In view of the versatile role of cold ions in building a quantum memory or processor, our experiment provides an alternative platform to explore PT\mathcal{PT}PT-symmetric physics and utilize pure quantum EP effects.
Observation of PT\mathcal{PT}PT-symmetry and exceptional point in ion trap
The theory of parity time (PT)(\mathcal{PT})(PT) symmetry has been quite successful in classical system. And classical PT\mathcal{PT}PT-symmetric systems exhibited many interesting features. However, PT\mathcal{PT}PT-symmetric experiments of quantum systems are progressing more slowly than PT\mathcal{PT}PT-symmetric experiments of classical systems. Hence, we constructed a passive quantum PT\mathcal{PT}PT-symmetric system by using the internal states of $ ^{40}Ca^{+}$ ion. Comparing with other systems, the experimental setup of single ion trap is easy to implement, meanwhile our single ion trap is a real quantum system and has a long coherence time. In this paper, we show the phenomenon of PT\mathcal{PT}PT-symmetry-breaking transions by controlling the dissipation factor of states, which is achieved through adjusting the power of laser beam. Moreover, we also investigated the quantum phase transition near exceptional point (EP) of PT\mathcal{PT}PT-symmetric system. The experimental results enable ion trap to be a successful device for investigating quantum PT\mathcal{PT}PT-symmetry.
Exceptional points (EPs) of a non-Hermitian Hamiltonian with parity-time-reversal (PT) symmetry have the potential to drastically enhance the capabilities of metrology and sensing through their power-law growing sensitivity to external perturbation. With the ability of generating and tuning dissipation in a single trapped ion system, we observe rich dynamics and detailed quantum phase transitions from the PT-symmetric phase to the symmetry-breaking phase. In this single qubit full quantum system, we develop a method to precisely determine the location of EP without any fitting parameter, and extract the eigenvalues in a unified way through all parameter regions. We can also obtain the full density matrix by quantum state tomography. Finally, we suggest from theoretical analysis that the periodically driving PT-symmetric non-Hermitian system can be used to measure the magnitude, frequency, and phase of time-dependent perturbation with EP enhancement.
Analysis of fundamentally open systems which exhibit both spatial reflection (parity) and time-reversal symmetry, called PT-symmetric [1] systems, has played an important role in understanding the dynamics of a broad class of non-Hermitian systems. Such systems support distinct regimes of stability and instability respectively, and the transition between these plays an important role in the system dynamics. We investigate a variety of non-Hermitian systems which exhibit a PT-symmetry breaking transition in both classical and quantum contexts using an array of theoretical and numerical approaches which are directly amenable to physical experiments. Organizationally, we divide these studies into those done on classical and quantum systems. Specifically for classical systems we analyze several interesting phenomena in the context of optical waveguide arrays. These provide an important testing ground for much of the discrete, PT-symmetric theory. In our case, we analyze PT-symmetric extensions of several interesting lattice models. Firstly, we explore single gain/loss pair, PT-symmetric extensions of the Su-Schreiffer-Heeger (SSH) model [2] and the Aubry-Andre-Harper (AAH) model [3,4]. In both cases, we find a veiled symmetry which is responsible for the PT-symmetry. Secondly we expand upon the Rudner-Levitov (RL) model [5,6], a non-Hermitian extension of the SSH model with multiple gain/loss pairs, and we explore the dependence of topological phenomena on changes in the initial state as well as their robustness in the presence of gain-induced nonlinearity. For quantum systems, we explore the rich PT-symmetric phase diagram resulting from time-periodic, Floquet PT-symmetry [7,8]. This is experimentally implementable in ultracold atomic systems [9], and features a reentrant PT-symmetric phase. Secondly, we examine quantum multi-photon statistics for a simple non-Hermitian model which is transformed and mapped to a system with unitary evolution via a unitary dilation, and is fully realizable on a small-scale quantum simulator [10].
Non-Hermitian systems satisfying parity-time (PT) symmetry have aroused considerable interest owing to their exotic features. Anti-PT symmetry is an important counterpart of the PT symmetry, and has been studied in various classical systems. Although a Hamiltonian with anti-PT symmetry only differs from its PT-symmetric counterpart in a global ±i phase, the information and energy exchange between systems and environment are different under them. It is also suggested theoretically that anti-PT symmetry is a useful concept in the context of quantum information storage with qubits coupled to a bosonic bath. So far, the observation of anti-PT symmetry in individual quantum systems remains elusive. Here, we implement an anti-PT-symmetric Hamiltonian of a single qubit in a single trapped ion by a designed microwave and optical control-pulse sequence. We characterize the anti-PTphase transition by mapping out the eigenvalues at different ratios between coupling strengths and dissipation rates. The full information of the quantum state is also obtained by quantum state tomography. Our work allows quantum simulation of genuine open-system feature of an anti-PT-symmetric system, which paves the way for utilizing non-Hermitian properties for quantum information processing.
Abstract We study the dynamics of correlations in a paradigmatic setup to observe PT -symmetric physics: a pair of coupled oscillators, one subject to a gain one to a loss. Starting from a coherent state, quantum correlations (QCs) are created, despite the system being driven only incoherently, and can survive indefinitely. Both total and QCs exhibit different scalings of their long-time behavior in the PT -broken/unbroken phase and at the exceptional point (EP). In particular, PT symmetry breaking is accompanied by non-zero stationary QCs. This is analytically shown and quantitatively explained in terms of entropy balance. The EP in particular stands out as the most classical configuration, as classical correlations diverge while QCs vanish.
Trapped ions are an ideal platform to implement quantum simulation. Previously, the parity-time (PT\mathcal{PT}PT)-reversal symmetry-breaking transition in the paradigmatic non-Hermitian Hamiltonian ${h}_{\mathcal{PT}}=J{\ensuremath{\sigma}}_{x}\ensuremath{-}i\mathrm{\ensuremath{\Gamma}}{\ensuremath{\sigma}}_{z}$ was observed in a single-ion experiment in a passive way. In this work we propose to study the interaction effects on the PT\mathcal{PT}PT-symmetry-breaking transition in a chain of NNN trapped interacting ions. We consider an effective Ising interaction ${H}_{\text{int}}^{\text{Ising}\phantom{\rule{4.pt}{0ex}}x}={\ensuremath{\sum}}_{j<k}{U}_{jk}{\ensuremath{\sigma}}_{x}^{j}{\ensuremath{\sigma}}_{x}^{k}$ between the ions on top of hPT{h}_{\mathcal{PT}}hPT​. We find that sufficiently strong interaction strength can enhance the PT\mathcal{PT}PT-symmetric phase for even NNN, while the phase is suppressed in all the other cases. In particular, the suppression can be so strong that even infinitesimal dissipation, quantified by $\mathrm{\ensuremath{\Gamma}}$, can turn the system into the PT\mathcal{PT}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.