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arXiv:2604.21320

Observation of quantum multi-Mpemba effect in a trapped-ion system

Gang Xia, Yu-Jie Zheng, Jing Huang, Chun-Wang Wu, Yi Xie, Ting Chen, Wei Wu, Weibin Li, Hui Jing, Jie Zhang, Yan-Li Zhou, Ping-Xing Chen

quant-phSubmitted Apr 23, 2026• Announced Apr 24, 2026• 0 citations
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Abstract

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.

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Theory of Quantum Imaginary-Time Mpemba Effect

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Quantum imaginary-time evolution (QITE) is a fundamental framework for preparing ground and thermal states, yet its computational cost scales significantly with the evolution duration $τ$. Reducing this duration is critical for practical quantum advantage. Here, we establish a unified theoretical framework for the Mpemba effect in QITE -- a counterintuitive phenomenon where a state initially farther from the ground state relaxes to it faster than one initially closer. We derive a remarkably simple necessary and sufficient condition for the occurrence of this effect, showing it is uniquely determined by the population ratios of excited states to the ground state. For practical state preparation, we introduce a rigorous sufficient condition for the finite-time Mpemba effect, ensuring the crossing occurs before reaching a prescribed proximity threshold. Furthermore, we unveil unique dynamical features, including a multiple-crossing phenomenon in multi-level systems and simultaneous intersections for collinear initial states. Our results provide criteria for identifying favorable initial states in QITE and offer deep insights into the speed limit of quantum state preparation.

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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 known 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 experimentally study the strong Mpemba effect in a single trapped ion system in which an exponentially accelerated relaxation in time is observed by preparing an optimal quantum initial state with no excitation of the slowest decaying mode. Also, we demonstrate 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 systems. Our work provides an efficient strategy to engineer the dynamics of open quantum system, and suggests a link unexplored yet between the Mpemba effect and the non-Hermitian physics. The Mpemba effect is an archetype for various anomalous relaxation phenomena. Here, the authors experimentally study a quantum version of the Mpemba effect in a single trapped ion system, where relaxation is exponentially accelerated by removing the excitation of the slowest decaying mode. This phenomenon, seen in Markovian open quantum systems containing Liouvillian exceptional points, indicates a link between the Mpemba effect and non-Hermitian physics.
Since its rediscovery in the twentieth century, the Mpemba effect, where a far-from-equilibrium state may relax faster than a state closer to equilibrium, has been extensively studied in classical systems and has recently received attention in quantum systems. Many theories explaining this counter-intuitive behavior in classical systems rely on memory effects. However, in quantum systems, the relation between the Mpemba effect and memory has remained unexplored. In this Letter, we consider general non-Markovian open quantum systems and reveal new classes of quantum Mpemba effects, with no analog in Markovian quantum dynamics. Generically, open quantum dynamics possess a finite memory time and a unique steady state. Because of non-Markovian dynamics, even if the system is initialized in the steady state it can take a long time to relax back. We find other initial states that reach the steady state much faster. Most notably, we demonstrate that there can be an initial state in which the system reaches the steady state within the finite memory time itself, giving the fastest possible relaxation to stationarity. We verify the effect for quantum dot systems coupled to electronic reservoirs in equilibrium and nonequilibrium setups at weak, intermediate and strong coupling. Our Letter provides new insights into the rich physics underlying accelerated relaxation in quantum systems.
The Mpemba effect (MpE), where a far-from-equilibrium state of a system relaxes faster compared to a state closer to it, is a well-known counterintuitive phenomenon in classical and quantum systems. Various system-specific theories have been proposed to explain this anomalous behavior in driven systems, though the fundamental mechanism of MpE in undriven systems, where MpE was first observed, remains unresolved. This paper provides a generic model of MpE for a quantum spin-1/21/21/2 system following Markovian relaxation dynamics, regardless of system structure or environment. The key lies in the overlap of initial states with the fast relaxation mode; here, the constituents create a fast decay mode via interaction through the shared environment to show MpE, indicating that MpE happens due to the collective behavior of the system. I also show that a system with anisotropic relaxation naturally exhibits MpE, even without a shared environment among the particles.
The Mpemba effect refers to the anomalous relaxation of a quantum state that, despite being initially farther from equilibrium, relaxes faster than a closer counterpart. Detecting such a quantum Mpemba effect typically requires full knowledge of the quantum state during its time evolution, which is an experimentally challenging task since state tomography becomes exponentially difficult as system size increases. This poses a significant obstacle in studying Mpemba effect in complex many-body systems. In this work, we demonstrate that this limitation can be overcome by identifying suitable observables that signal rapid relaxation. Moreover, as long as the system equilibrates to a known unique steady-state, it is possible to fully detect the occurrence of quantum Mpemba effect just by measuring the observable for known state preparations. Our approach thus significantly reduces experimental complexity and offers a practical route for observing the quantum Mpemba effect in complex and extended multi-qubit setups.
The quantum Mpemba effect refers to the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than one prepared closer to it. Several mechanisms have been identified in open quantum systems to explain this behavior, including the strong Mpemba effect, non-Markovian memory, and initial system-reservoir entanglement. Here, we unveil a distinct mechanism rooted in the non-normal nature of the Liouvillian superoperator in Markovian dynamics. When the Liouvillian's eigenmodes are non-orthogonal, transient interference between decaying modes can induce anomalous early-time behavior-such as delayed thermalization or transient freezing-even though asymptotic decay rates remain unchanged. This differs fundamentally from strong Mpemba effects, which hinge on suppressed overlap with slow-decaying modes. We demonstrate this mechanism using a waveguide quantum electrodynamics model, where quantum emitters interact with the photonic modes of a one-dimensional waveguide. The directional and radiative nature of these couplings naturally introduces non-normality into the system's dynamics. As a result, certain initial states-despite being closer to equilibrium-can exhibit slower relaxation at short times. This work reveals a previously unexplored and universal source of Mpemba-like behavior in memoryless quantum systems, expanding the theoretical framework for anomalous relaxation and opening new avenues for control in engineered quantum platforms.
Quantum imaginary-time evolution (QITE) is a fundamental framework for preparing ground and thermal states, yet its computational cost scales significantly with the evolution duration τττ. Reducing this duration is critical for practical quantum advantage. Here, we establish a unified theoretical framework for the Mpemba effect in QITE -- a counterintuitive phenomenon where a state initially farther from the ground state relaxes to it faster than one initially closer. We derive a remarkably simple necessary and sufficient condition for the occurrence of this effect, showing it is uniquely determined by the population ratios of excited states to the ground state. For practical state preparation, we introduce a rigorous sufficient condition for the finite-time Mpemba effect, ensuring the crossing occurs before reaching a prescribed proximity threshold. Furthermore, we unveil unique dynamical features, including a multiple-crossing phenomenon in multi-level systems and simultaneous intersections for collinear initial states. Our results provide criteria for identifying favorable initial states in QITE and offer deep insights into the speed limit of quantum state preparation.