Quantum Mpemba Effect Induced by Non-Markovian Exceptional Point

TL;DR

This work addresses QMPE beyond the Born–Markov approximation by formulating a non-Markovian LEP mechanism using the pseudomode master equation, which maps memory-bearing baths to an extended Lindbladian dynamics with auxiliary modes. By analyzing the Liouvillian spectrum, the authors show that non-Markovian LEPs can maximize the Liouvillian spectral gap Δ = -Re(λ1) and induce accelerated relaxation, yielding QMPE in a dissipative quantum harmonic oscillator. A Lorentzian spectral density example demonstrates explicit QMPE under γ = 4α, and contrasts with Markovian limits where no LEP or QMPE occurs. The results provide a unified framework for LEP–QMPE interplay, with experimental feasibility in NMR platforms and potential to enhance energy and information transfer in quantum technologies.

Abstract

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.

Figures (3)

• Figure 1: (a) Sketch of the pseudomode master equation approach and the cartoon of QMPE. An initial far-from equilibrium state $\varrho_{\text{s}}^{(1)}(0)$ can relax toward the equilibrium state faster than a closer-to-equilibrium initial state $\varrho_{\text{s}}^{(2)}(0)$. (b) The Liouvillian spectral analysis, the blue solid lines are $\text{Re}(\lambda_{\ell})$ and the green dashed lines are $\text{Im}(\lambda_{\ell})$. The LEPs are marked by red stars and one non-LEP is represented by the blue circle. (c) A QMPE can be observed by using non-Markovian LEPs.
• Figure 2: (a) The Liouvillian spectral gap for the dissipative quantum harmonic oscillator model. A LEP occurs at $\gamma=4\alpha$. (b) The trace distance $D(t)$ is plotted as a function of $\omega_{0}t$ with different decay rates: $\gamma=4\alpha$ (red stars), $\gamma=6\alpha$ (green diamonds) and $\gamma=2\alpha$ (blue rectangles). Other parameters are chosen as $\omega_{0}=1~\text{cm}^{-1}$ and $\alpha/\omega_{0}=1$.
• Figure 3: (a) Real part of the eigenvalues of the extended Liouvillian superoperator with $\gamma=\omega_{0}$. The green solid lines are non-Markovian results and blue dashed line is the Markovian result. (b) $\ln D(t)$ versus $\omega_{0}t$ for the non-Markovian (red solid line) and the Markovian (blue dashed line) results with $\gamma=10\omega_{0}$ and $\alpha/\omega_{0}=2.5$. The green squares (magenta circles) are analytical results from the Liouvillian spectral gap with $\Delta=\frac{1}{4}\gamma-\frac{1}{4}\sqrt{\gamma^{2}-16\alpha^{2}}$ ($\Delta_{\text{M}}=\frac{1}{2}\gamma_{\text{M}}$). (c-d) $D(t)$ versus $\omega_{0}t$ with $\alpha/\omega_{0}=2.4$ (blue lines) and $\alpha/\omega_{0}=2.5$ (red lines). The solid lines are the non-Markovian results, while the dashed lines are the predictions by the Born-Markovian approximation. Other parameters are chosen as $\xi_{1}=2$, $\xi_{2}=1$, $\gamma=10\omega_{0}$ and $\omega_{0}=1~\text{cm}^{-1}$.