Quantum refrigerator embedded in spin-star environments: Scalings of temperature and refrigeration time

TL;DR

This paper investigates a quantum refrigerator with three qubits in spin-star environments, highlighting transient cooling, non-Markovian effects, and how optimal temperature and cooling time scale with environmental spins.

Contribution

It introduces a model of a quantum refrigerator with non-Markovian spin-star environments, deriving scaling laws for temperature and cooling time based on environmental size.

Findings

Transient cooling occurs without steady-state achievement.

Optimal cold qubit temperature approaches a constant as environment grows.

Minimum cooling time scales with the number of bath spins.

Abstract

We examine a quantum absorption refrigerator that comprises three qubits, each of which is connected with a separate spin-star environment. The refrigerator exhibits the feature of transient cooling, i.e., lowering of the temperature of the first qubit in sufficiently small timescales. Since the spin-star environment is inherently non-Markovian in nature, steady-state cooling is not achieved. A key advantage of our model is that the symmetries of the Hamiltonian enable a solution of the reduced density matrices of the refrigerator qubits, even in the presence of a large number of environmental spins. We derive the condition for autonomous refrigeration and analyze how the optimal cold qubit temperature scales with the number of bath qubits. We find a power law scaling towards a constant asymptotic value. We also find the scaling of the minimum time required for cooling as a function of the number of bath spins. Further, we scrutinize the heat currents associated with each of the three qubits.