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arXiv:2304.06590

Observation of quantum temporal correlations well beyond Luders bound

Chun-Wang Wu, Zhang, Man-Chao, Yanli Zhou, Ting Chen, Ran Huang, Yi Xie, Bao-Quan Ou, Wei Wu, Adam Miranowicz, Franco Nori, Jie Zhang, Hui Jing, Ping‐Xing Chen

Published Apr 13, 2023• 1 citation
arXivHTMLPDF

Abstract

Quantum correlations, both spatial and temporal, are the central pillars of quantum mechanics. Over the last two decades, a big breakthrough in quantum physics is its complex extension to the non-Hermitian realm, and dizzying varieties of novel phenomena and applications beyond the Hermitian framework have been uncovered. However, unique features of non-Hermitian quantum correlations, especially in the time domain, still remain to be explored. Here, for the first time, we experimentally achieve this goal by using a parity-time (PT)-symmetric trapped-ion system. The upper limit of temporal quantum correlations, known as the algebraic bound, which has so far not been achieved in the standard measurement scenario, is reached here by approaching the exceptional point (EP), thus showing the unexpected ability of EPs in tuning temporal quantum correlation effects. Our study, unveiling the fundamental interplay of non-Hermiticity, nonlinearity, and temporal quantum correlations, provides the first step towards exploring and utilizing various non-Hermitian temporal quantum effects by operating a wide range of EP devices, which are important for both fundamental studies and applications of quantum EP systems.

DOI
10.48550/arxiv.2304.06590

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Quantum correlations, both spatial and temporal, are the central pillars of quantum mechanics. Over the last two decades, a big breakthrough in quantum physics is its complex extension to the non-Hermitian realm, and dizzying varieties of novel phenomena and applications beyond the Hermitian framework have been uncovered. However, unique features of non-Hermitian quantum correlations, especially in the time domain, still remain to be explored. Here, for the first time, we experimentally achieve this goal by using a parity-time (PT)-symmetric trapped-ion system. The upper limit of temporal quantum correlations, known as the algebraic bound, which has so far not been achieved in the standard measurement scenario, is reached here by approaching the exceptional point (EP), thus showing the unexpected ability of EPs in tuning temporal quantum correlation effects. Our study, unveiling the fundamental interplay of non-Hermiticity, nonlinearity, and temporal quantum correlations, provides the first step towards exploring and utilizing various non-Hermitian temporal quantum effects by operating a wide range of EP devices, which are important for both fundamental studies and applications of quantum EP systems.
Abstract The powerful ability of achieving and manipulating strong spatial quantum correlations has helped the emergence of quantum information science. In contrast, strong temporal quantum correlations (TQC), playing an essential role in a wide range of physical and biological processes, have remained an elusive and long-standing challenge, hindering their practical applications. Here, for the first time, we experimentally demonstrate how to break the Lüders bound and to achieve the ultimate upper limit of TQC, by using a parity-time (PT)-symmetric single-ion system, within a standard measurement scenario. We achieve this goal by approaching an exceptional point (EP) in such a system, confirming the power of PT symmetry and non-Hermitian phase transition in enhancing purely quantum effects. Our work not only removes an important obstacle for TQC-based quantum engineering applications, but also sheds new light on operating quantum devices at EPs.
The ability of achieving strong quantum spatial correlations has helped the emergence of quantum information science. In contrast, how to achieve strong quantum temporal correlations (QTCs) has remained as a long-standing challenge, thus hindering their applications in time-domain quantum control. Here we experimentally demonstrate that by using a parity-time ( PT )–symmetric single ion, the conventional QTC limit known as the Lüders bound can be well surpassed within a standard measurement scenario, approaching the predicted maximum QTC value. Our work, as a step toward quantum engineering of PT devices in the time domain, can stimulate more efforts on operating various quantum devices with the aid of strong QTC resources.
The Leggett-Garg inequality (LGI) delineates a boundary between quantum and classical systems. While the temporal quantum correlations represented by LGIs have been extensively investigated in the Hermitian domain, the exploration of LGIs under non-Hermitian conditions remains scarce. Theoretical conjectures posit that nonunitary dynamics could transcend the boundary of LGIs set by Hermitian quantum mechanics, yet its empirical validation is lacking. Here, we demonstrate the enhanced violation of LGIs in a non-Hermitian system of a parity-time (PT\mathcal{PT}PT)-symmetric trapped-ion qubit. The upper bounds of both the third-order parameter K3{K}_{3}K3​ and fourth-order parameter K4{K}_{4}K4​ increase with dissipation and can reach the maximum value when the system approaches the exceptional point, where ${K}_{3}={C}_{21}+{C}_{32}\ensuremath{-}{C}_{31}$ is comprising three two-time correlations and ${K}_{4}={C}_{21}+{C}_{32}+{C}_{43}\ensuremath{-}{C}_{41}$ is comprising four correlations. We also find that the lower bounds of K3{K}_{3}K3​ and K4{K}_{4}K4​ exhibit distinctive behaviors, where the lower bound of K3{K}_{3}K3​ remains constant, but that of K4{K}_{4}K4​ depends on the target states and measurement operators. These findings reveal a pronounced correlation between the dissipative nature of a quantum system and its temporal correlations.
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.
Exceptional points (EPs), the degeneracy points of non-Hermitian systems, have recently attracted great attention because of their potential of enhancing the sensitivity of quantum sensors. Unlike the usual degeneracies in Hermitian systems, at EPs, both the eigenenergies and eigenvectors coalesce. Although EPs have been widely explored, the range of EPs studied is largely limited by the underlying systems, for instance, higher-order EPs are hard to achieve. Here we propose an extendable method to simulate non-Hermitian systems and study EPs with quantum circuits. The system is inherently parity-time (PT) broken due to the non-symmetric controlling effects of the circuit. Inspired by the quantum Zeno effect, the circuit structure guarantees the success rate of the post-selection. A sample circuit is implemented in a quantum programming framework, and the phase transition at EP is demonstrated. Considering the scalable and flexible nature of quantum circuits, our model is capable of simulating large-scale systems with higher-order EPs.
Quantum theory provides rules governing much of the microscopic world, and among its counter-intuitive consequences are correlations that exceed the bounds from local, classical theories. In two-level quantum systems - qubits - unitary dynamics theoretically limit these spatiotemporal quantum correlations, called Bell/Clauser-Horn-Shimony-Holt or Leggett-Garg inequalities, to 222\sqrt{2}22​ or 1.5 respectively. Experiments with state-of-the-art qubits have approached the spatial, Bell and temporal, Leggett-Garg quantum correlation bounds. Here, using a dissipative, trapped 40^{40}40Ca+^++ ion governed by a two-level, non-Hermitian Hamiltonian, we observe temporal correlation values up to 1.703(4) for the Leggett-Garg parameter K3K_3K3​, clearly exceeding the hitherto inviolable Lüder's bound of 1.5. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics. Distinct evolution speeds for antipodal qubit states, which violate the unified (Mendelstam-Tamm or Margolus-Levitin) bound τQSLτ_{\textrm{QSL}}τQSL​ for the transit time based on quantum speed limit, result in the super-quantum K3K_3K3​ values observed over a wide parameter range. Our results demonstrate that post-selected, coherent dynamics of non-Hermitian Hamiltonians pave the way for enhanced quantum correlations that exceed protocols based on unitary or dissipative dynamics.