Quantum Mpemba effect describes an anomalous phenomenon of accelerated relaxation which is of fundamental interest in the field of nonequilibrium thermodynamics. Conventional theories on this phenomenon strongly rely on the Born-Markovian approximation, but this effect is not well understood in non-Markovian regimes. By investigating the relaxation process within the framework of a general non-Markovian dynamics, we propose a mechanism of realizing the quantum Mpemba effect via non-Markovian exceptional points. We verify the feasibility of this mechanism in a dissipative quantum harmonic oscillator model. Providing a new insight into the interesting non-equilibrium dynamics phenomenon, our work paves a way to accelerate the transfer of energy and information in quantum systems.
Quantum Mpemba effect describes an anomalous phenomenon of accelerated relaxation which is of fundamental interest in the field of nonequilibrium thermodynamics. Conventional theories on this phenomenon strongly rely on the Born-Markovian approximation, but this effect is not well understood in non-Markovian regimes. By investigating the relaxation process within the framework of a general non-Markovian dynamics, we propose a mechanism of realizing the quantum Mpemba effect via non-Markovian exceptional points. We verify the feasibility of this mechanism in a dissipative quantum harmonic oscillator model. Providing a new insight into the interesting non-equilibrium dynamics phenomenon, our work paves a way to accelerate the transfer of energy and information in quantum systems.
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.
The quantum Mpemba effect (QMPE), an anomalous relaxation phenomenon, has been demonstrated in both closed and open Hermitian quantum systems. While some studies have linked the QMPE to Liouvillian exceptional points---non-Hermitian features emerged at the Liouvillian level---in open Hermitian quantum systems, it remains largely unexplored whether the QMPE can occur in intrinsic non-Hermitian systems, where non-Hermiticity is inherent at the Hamiltonian level. Here, we demonstrate unequivocally the occurrence of QMPE in experimentally realizable parity-time symmetric qubit systems immersed in a bosonic bath. Using established quantifiers for QMPE, we show numerically that the QMPE persists across parameter regimes both near and far from Hamiltonian and Liouvillian exceptional points, but disappears entirely when a Hermitian Hamiltonian is restored. Interestingly, neither Hamiltonian nor Liouvillian exceptional points demarcate the boundaries of the QMPE regime. To complement numerical results, we develop an analytical description based on a long-time approximation of the relaxation dynamics of quantifiers. This approach allows us to decipher the number of intersections between two dynamical trajectories of quantifier starting from two initial conditions in the validity regime of the long-time approximation, thereby providing additional information that delineates the parameter regimes supporting the genuine QMPE. We further demonstrate the robustness of QMPE against increasing the number of qubits and dephasing effect. Our findings not only broaden the scope of the QMPE but also suggest its intricate interplay with non-Hermitian features beyond exceptional points.
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 quantum Mpemba effect concerns with anomalous relaxation of quantum states that evolves either under unitary or non-unitary dynamics. In the context of open quantum systems, while most studies focus on quantum states evolving under completely positive trace-presing dynamics described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, we demonstrate that an analogous effect can arise at the level of operators. In particular, we show that operators that evolves under the adjoint Liouvillian -- despite not being a trace-preserving map -- can still exhibit a genuine Mpemba effect. We derive general conditions under which this phenomenon can occur and validate our predictions for three different open quantum setups. Our results broaden the scope of the Mpemba effect in quantum systems and provide a framework for controlling the relaxation of physically relevant observables.
The behavior of systems far from equilibrium is often complex and unpredictable, challenging and sometimes overturning the physical intuition derived from equilibrium scenarios. One striking example of this is the Mpemba effect, which implies that non-equilibrium states can sometimes relax more rapidly when they are further from equilibrium. Despite a rich historical background, the precise conditions and mechanisms behind this phenomenon remain unclear. Recently, there has been growing interest in investigating accelerated relaxation and Mpemba-like effects within quantum systems. In this work, we explore a quantum manifestation of the Mpemba effect in a simple and paradigmatic model of open quantum systems: the damped quantum harmonic oscillator, which describes the relaxation of a bosonic mode in contact with a thermal bath at finite temperature T . By means of an exact analytical analysis of the relaxation dynamics based on the method of moments in both population and coherence subspaces, we demonstrate that any initial distribution of populations with the first r moments exactly matching those of the equilibrium distribution shows a super-accelerated relaxation to equilibrium at a rate linearly increasing with r , leading to a pronounced Mpemba effect. In particular, one can find a broad class of far-from-equilibrium distributions that relax to equilibrium faster than any other initial thermal state with a temperature T ′ arbitrarily close to T . The super-accelerated relaxation effect is shown to persist even for a broad class of initial states with non-vanishing coherences, and a general criterion for the observation of super-accelerated thermalization is presented.