Accelerating Quantum Relaxation via Temporary Reset: A Mpemba-Inspired Approach

Abstract

Slow relaxation processes spanning widely separated timescales pose fundamental challenges for probing steady-state properties and engineering functional quantum systems, such as quantum heat engines and quantum computing devices. We introduce a protocol that enables significant acceleration of relaxation in general Markovian open quantum systems by temporarily coupling the system to a reset channel, inspired by the Mpemba effect. Crucially, this acceleration persists even when the slowest decaying Lindbladian modes form complex-conjugate pairs. Unlike previous approaches, which typically target a single mode, our protocol may suppress multiple relaxation modes simultaneously. This framework provides a versatile and experimentally feasible tool for controlling relaxation timescales, with broad implications for quantum thermodynamics, computation, and state preparation.

Figures (3)

• Figure 1: Relaxation dynamics of the two-state system. (a) and (c): Distances between $\rho(t)$ and $\rho_{\text{eq}}$ as a function of time $t$ with different resetting rates $r$. (b) and (d): The $t_{s}$ as a function of the resetting rate $r$. The parameters are chosen as $\beta_{0}=2.0$, $k=0.32$ and $\phi=1$ with reset protocol and $\beta_{0}=3.0,$$k=0.21$ and $\phi=1$ without reset. The environment is at lower temperature $\beta_{\text{env}}=4.0$. $\gamma_1=1.0$. For (a) and (b) $\Omega=0$, for (c) and (d) $\Omega=2.0$.
• Figure 2: Acceleration of the relaxation of TFIMs. Reset rates $r$ are chosen as $0, 1.0, 5.0, 10.0, 20.0$. (a) $N=5$ ($d=32$), $\alpha=0.55$, $t_s=0.08\tau_2$. (b) $N=5$, $\alpha=0.05$, $t_s=0.50\tau_2$. (c) $N=6$ ($d=64$), $\alpha=0.55$, $t_s=0.08\tau_2$. (d) $N=6$, $\alpha=0.05$, $t_s=0.50\tau_2$. The vertical gray lines mark $t_s$ at which the reset channel is removed. Inset: Schematic representation of the dissipative TFIM, with each spin coupled to a thermal bath.
• Figure 3: Dephasing noise induces acceleration of relaxation in a 5-site TFIM. Parameters: (a) $J=1.0, \ g=2.0,\ \gamma =0.5,\ \beta=0.1J,\ t_s=0.2\tau_2$ (b) $J=1.0, \ g=2.0,\ \gamma =0.5,\ \beta=0.1J,\ t_s=0.8\tau_2$.