A General Strategy for Realizing Mpemba Effects in Open Quantum Systems

Abstract

The Mpemba effect, where a state farther from equilibrium relaxes faster than one closer to it, is a striking phenomenon in both classical and quantum systems. In open quantum systems, however, the quantum Mpemba effect (QME) typically occurs only for specifically chosen initial states, which limits its universality. Here we present a general and experimentally feasible strategy to realize both QME and anti-QME. By applying a temporary bond-dissipation quench, we selectively suppresses or enhances slow relaxation modes, thereby reshaping relaxation pathways independently of both the system and the initial state. We demonstrate this mechanism in systems with dephasing and boundary dissipation, and outline feasible cold-atom implementations. Our results establish controllable dissipation as a versatile tool for quantum control, accelerated relaxation, and efficient nonequilibrium protocols.

Figures (4)

• Figure 1: Schematic illustration of the QME. (a) Natural relaxation (orange) is dominated by the slowest Liouvillian mode, while the alternative trajectory (orange dashed) bypasses this mode and reaches the steady state faster. (b) Time evolution of two initial states: although the red state starts farther from the steady state, applying bond dissipation (yellow-shaded region) accelerates its relaxation so that it overtakes the blue state, demonstrating the QME.
• Figure 2: QME induced by a temporary bond-dissipation quench under dephasing dissipation. (a) Initial states: $\rho_1$ (localized, far from equilibrium) and $\rho_2$ (less localized, closer to equilibrium). (b) Time evolution of the trace distance $D^{(i)}(t)$, where the blue (orange) solid line corresponds to the initial state $\rho_1(0)$ [$\rho_2(0)$]. A short bond dissipation quench ($t_1=45$, $t_2=65$) accelerates the relaxation of $\rho_1$ (blue dashed line). (c) Time evolution of the slowest-mode amplitude $|\mu_1|$ corresponding to the three cases in (b). Other parameters: $\gamma^d=0.01$, $\Gamma=0.01$, $p=1$, $a=1$.
• Figure 3: Boundary dissipation with a temporary bond-dissipation quench. (a) Initial states $\rho_1(0)=|5\rangle\langle 5|$ and $\rho_2(0)=|9\rangle\langle 9|$. (b) Time evolution of the trace distance $D^{(i)}(t)$. With bond dissipation, $\rho_2$ relaxes faster for $a=-1,p=2$ (orange dashed line, QME), while $\rho_1$ relaxes more slowly for $a=1,p=2$ (blue dashed line, anti-QME). (c) Time evolution of the slowest-mode amplitude $|\mu_1|$ for the cases in (b). (d) Time evolution of the next-slowest mode amplitude $|\mu_2|$. (e) Time evolution of intermediate modes $|\mu_j|$ with $j = 45$ to $54$. Here $\Gamma=0.4$, $\gamma^b_1=\gamma^b_L=0.2$, $t_1=0.5$ and $t_2=3$.
• Figure 4: Experimental schemes. (a) Realization of local dephasing (via a weak $\pi$-polarized beam) and nearest-neighbor ($p=1$) bond dissipation (via $\sigma^+$-polarized driving), using a state-dependent auxiliary lattice. (b) Setup for boundary loss combined with next-nearest-neighbor ($p=2$) bond dissipation, employing a spin-dependent ground-state lattice and an auxiliary lattice shifted by half a period.