The Mpemba effect in quantum oscillating and two-level systems

TL;DR

This paper investigates the Mpemba effect in quantum oscillating and two-level systems, deriving exact solutions and analyzing the conditions under which the effect occurs, including potential for experimental observation.

Contribution

It introduces a novel analytical approach to study the Mpemba effect in quantum systems, deriving exact density matrices and identifying conditions for the effect in various quantum states.

Findings

Number states intersect with coherent states earlier for smaller N.

Thermal states intersect with coherent states at specific parameters.

The Mpemba effect is demonstrated in quantum two-level systems.

Abstract

The Empemba effect (ME) is investigated in the context of ubiquitous quantum oscillating and two-level systems (TLS) using a novel approach (DOI 10.1088/1402-4896/ad97f1). Exact reduced density matrices for various initial states are derived. The temporal behavior of the trace distance for these initial states is calculated analytically and presented. For a dissipative quantum oscillating system, it is demonstrated that number states $|N\rangle$ intersect with coherent states $|\alpha\rangle$, with this intersection occurring earlier for smaller values of $N$. Additionally, thermal states intersect with coherent states for specific values of $|\alpha|$, leading to the occurrence of the ME in these two scenarios. A weaker version of the ME is also observed for thermal and number states. In the case of a quantum TLS, it is shown that the ME effect occurs, and the potential for its realization and experimental observation is discussed, with reference to the Jaynes-Cummings model (JCM) involving a decaying time-dependent coupling function.