Unraveling the Quantum Mpemba Effect on Markovian Open Quantum Systems

TL;DR

The paper investigates the quantum Mpemba effect (QME) in Markovian open quantum systems, seeking mechanisms that allow an out-of-equilibrium state to thermalize faster than a closer-to-equilibrium counterpart. It develops multiple viewpoints: a decoherence-free-subspace (DFS) mechanism that creates fast and slow decay channels, an extreme QME where relaxation accelerates with system size, and a trajectory-based analysis of Davies-map dynamics to illuminate how jump processes and coherences shape the effect. It also introduces a microscopic bosonic Gaussian-bath model to show how bath correlations and reduced coherences can accelerate thermalization, supporting the proposed mechanisms. The results highlight how control over dissipation channels, system size, and bath structure can engineer faster thermalization in quantum technologies, with potential impacts on quantum optics and ultracold-gas platforms.

Abstract

In recent years, the quantum Mpemba effect (QME), which occurs when an out-of-equilibrium system reaches equilibrium faster than another that is closer to equilibrium, has attracted significant attention from the scientific community as an intriguing and counterintuitive phenomenon. It generalizes its classical counterpart by extending the concept beyond temperature equilibration. This paper approaches the QME in Markovian open quantum systems from different perspectives. First, we propose a physical mechanism based on decoherence-free subspaces. Second, we show that an exponential enhancement of the decay rate toward equilibrium, scaling with system size, can be obtained, leading to an extreme version of the phenomenon in Markovian open quantum systems. Third, we study the strong Mpemba effect through the unravelings of Davies maps, revealing subtleties in the choice of figures of merit used to identify the QME. Finally, we propose a microscopic model to gain deeper insight into bath dynamics in this context.

Figures (13)

• Figure 1: Illustrative picture of the quantum Mpemba effect.
• Figure 2: Evolution of the non-equilibrium free energy (a) and trace distance (b) for the states $\rho$ and $\rho' = U \rho U^{\dagger}$. The state $\rho'$ is observed to exhibit lower values of $F_{\mathrm{neq}}$ and $d_{\mathrm{Tr}}$ than $\rho$ after a certain elapsed time, characterizing the quantum Mpemba effect in this system. The parameters used are $\omega = 5$, $\gamma_+ = \gamma_- = 1$, and $T = 10\gamma_+$. The initial state $\rho$ is defined by the Bloch vector $\boldsymbol{R} = (0.52807291, 0.21585042, 0.02214326)$.
• Figure 3: (a) Non-equilibrium free energy for triplet (red line) and singlet (black line) for evolution under collective decay. The result shows that the singlet state is trapped in its initial state if no local dissipator is used ($\mu = 0$) and $J_z = 5$. (b) Same parameters, but with $\mu = 1$.
• Figure 4: Non-equilibrium free energy for the all-up state (red line) and decoherence-free subspace state (black line) for evolution under collective dissipation at 3 different temperatures, where $T = 0\Gamma, 1\Gamma, \text{ and } 10\Gamma$ for (a), (b), and (c), respectively. Here, the parameters used were $J_z = 5$, $\Gamma = 1$, and $\mu = 1$.
• Figure 5: Non-equilibrium free energy for the all-up state (red line) and decoherence-free subspace state (black line) for evolution under collective dissipation at temperature $T = 1\Gamma$. Here, the parameters used were $J_z = 5$, $\Gamma = 1$, and $\mu = 0.5$.