Mpemba effect in self-contained quantum refrigerators: Accelerated cooling

TL;DR

This paper demonstrates the quantum Mpemba effect in a self-contained qubit-qutrit refrigerator, showing that certain initial states can reach steady cooling faster, with implications for accelerated quantum thermal processes.

Contribution

It reveals the presence of the quantum Mpemba effect in a qubit-qutrit system and analyzes how initial states and system-bath interactions influence accelerated cooling.

Findings

Quantum Mpemba effect observed in the refrigerator model.

Mpemba states can be generated by local and global unitaries.

System-bath coupling affects the occurrence of the Mpemba effect.

Abstract

We consider the qubit-qutrit model of self-contained quantum refrigerator and observe the quantum Mpemba effect in its cooling. In this system, the qutrit acts as the refrigerator while the qubit is to be cooled. The entire system is coupled to three bosonic heat baths, due to which the dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation. We investigate the Liouvillian that generates the dynamics of the system and find that it has a block diagonal form. The dynamics of each element of the system's density matrix can be determined by solving the dynamical equation of the corresponding block that contains it. We find that the steady state belongs to the block containing only the diagonal elements in the energy basis. We numerically solve for the steady state and investigate the steady-state cooling over a significant region of the parameter space. Moreover, we demonstrate the quantum Mpemba effect in the refrigerator: a Mpemba state obtained by applying a unitary on the equilibrium state of the system reaches the steady state faster than the equilibrium state, despite the Mpemba state being initially farther away from the steady state. The Mpemba state thus leads to an acceleration in cooling of the cold qubit. We also find that both local and global unitaries on the qubit-qutrit system can generate the Mpemba state. Finally, we study the effect of the system-bath couplings on the Mpemba effect.