Yan-Li Zhou

The quantum Mpemba effect (ME) in Markovian systems is conventionally explained by a smaller overlap between the initial state and the slowest decay mode (SDM). Such state, initially farther away from equilibrium or steady state, relaxes faster than closer ones, resulting to a crossing of their trajectories. This picture, by neglecting the transient dynamics, holds in the long-time limit. Here we experimentally observe multiple trajectory crossings (multi-ME) in the relaxation dynamics of a trapped ion. Such novel dynamics takes place in a unusual scenario where the initial state instead has a larger overlap with the SDM. We develop a theoretical framework based on relaxation speed to understand the multi-ME. We show that the initial relaxation speed is governed by the fastest decay mode, which together with the SDM overlap gives a phase diagram that reveals both the occurrence and the types of quantum ME observed in our experiment. Our study goes beyond the simple picture based on the long-time limit, tracks continuously the quantum ME dynamics, and establishes a comprehensive framework to describe the transient quantum relaxation.

An ancient and counterintuitive phenomenon know as the Mpemba effect (water can cool faster when initially heated up) showcases the critical role of initial conditions in relaxation processes. How to realize and utilize this effect for speeding up relaxation is an important but challenging task in purely quantum system till now. Here, we report the first experiment, as far as we know,about the strong Mpemba effect in a single trapped ion system in which an exponentially expedited relaxation in time is observed by preparing an optimal initial state with no excitation of the slowest decaying mode. Also, we find that the condition of realizing such effect coincides with the Liouvillian exceptional point, featuring the coalescence of both the eigenvalues and the eigenmodes of the system. Our work provides an efficient strategy to exponentially accelerate relaxations of quantum system to their stationary state, and suggests a link unexplored yet between the Mpemba effect and the non-Hermitian physics. It could open up the door to engineer a wide range of dissipative quantum systems by utilizing the anomalous Mpemba effect, for applications in quantum simulation and quantum information processing.

We investigate speeding up of relaxation of Markovian open quantum systems with the Liouvillian exceptional point (LEP), where the slowest decay mode degenerate with a faster decay mode. The degeneracy significantly increases the gap of the Liouvillian operator, which determines the timescale of such systems in converging to stationarity, and hence accelerates the relaxation process. We explore an experimentally relevant three level atomic system, whose eigenmatrices and eigenspectra are obtained completely analytically. This allows us to gain insights in the LEP and examine respective dynamics with details. We illustrate that the gap can be further widened through Floquet engineering, which further accelerates the relaxation process. Finally, we extend this approach to analyze laser cooling of trapped ions, where vibrations (phonons) couple to the electronic states. An optimal cooling condition is obtained analytically, which agrees with both existing experiments and numerical simulations. Our study provides analytical insights in understanding LEP, as well as in controlling and optimizing dissipative dynamics of atoms and trapped ions.

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.

Parity-time($\mathcal{PT}$)-symmetric systems, featuring real eigenvalues despite its non-Hermitian nature, have been widely utilized to achieve exotic functionalities in the classical realm, such as loss-induced transparency or lasing revival. By approaching the exceptional point (EP) or the coalescences of both eigenvalues and eigenstates, unconventional effects are also expected to emerge 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 quantum memory or processor, our experiment provides a new platform to explore and utilize pure quantum EP effects, with diverse applications in quantum engineering of trapped ions.