Thermal state preparation by repeated interactions at and beyond the Lindblad limit

TL;DR

This paper investigates the dynamics of thermal state preparation via repeated interactions, revealing a Mpemba-like effect where higher-temperature states sometimes take longer to thermalize, with analytical insights and implications for large systems.

Contribution

It provides analytical expressions for minimal simulation time in repeated interaction protocols and uncovers a Mpemba-like effect in thermalization dynamics.

Findings

Derived closed-form expressions for minimal collision number to reach thermal states.

Identified conditions minimizing simulation time at zero temperature.

Discovered and analytically characterized the Mpemba-like effect in thermalization.

Abstract

We study the nature of thermalization dynamics and the associated preparation (simulation) time under the repeated interaction protocol uncovering a generic anomalous, Mpemba-like trend. As a case study, we focus on a three-level system and analyze its dynamics in two complementary regimes, where the system-ancilla interaction strength is either large or small. Focusing on the estimation of the simulation time, we derive closed-form expressions for the minimum number of collisions, or minimal simulation time, required to achieve a thermal state, which is within $\epsilon$ distance to the target thermal state. At zero temperature, we analytically identify a set of points (interaction strength $\times$ their duration) that minimize the simulation time. At nonzero temperature, we observe a Mpemba-like effect: Starting from a maximally mixed state, thermalization to an intermediate-temperature state takes longer than to a lower-temperature one. We provide an accurate analytical approximation for this phenomenon and demonstrate its occurrence in larger systems and under randomized interaction strengths. The prevalence of the Mpemba effect in thermal state preparation presents a significant challenge for preparing states in large systems, an open problem calling for new strategies.