Designing refrigerators in higher dimensions using quantum spin models

TL;DR

This paper explores the design of quantum refrigerators using higher-dimensional spin models, demonstrating performance improvements with increased spin dimension and introducing a novel local temperature measure applicable to arbitrary spins.

Contribution

It introduces a distance-based local temperature measure for arbitrary spin quantum numbers and shows performance enhancement in quantum refrigerators with higher spin dimensions.

Findings

Performance of quantum refrigerators improves with higher spin dimension.

The new local temperature measure aligns with existing definitions for spin-1/2.

Refrigerators with mixed spins can achieve lower local temperatures.

Abstract

We design quantum refrigerators based on spin-j quantum XYZ and bilinear-biquadratic models with individual spins attached to bosonic thermal baths. By considering both local and global master equations, we illustrate an enhancement in the performance of the refrigerators with an increase in the spin dimension irrespective of the choice of the spin models. To assess the performance of the refrigerators, we introduce a distance-based measure to quantify the local temperature of a particle with arbitrary spin quantum number j. Interestingly, we find that the local temperature quantifier, defined via minimizing the distance between a spin-j thermal state and the evolved state of the spin-j particle in the steady state, coincides with the population-based definition of local temperature known in the literature for spin-1/2 particles. Moreover, we demonstrate that the qualitative behavior of the distance-based local temperature is independent of the choice of the distance measure by comparing the trace distance, Uhlmann's fidelity and relative entropy distance. We further observe by computing local master equation that the quantum refrigerator consisting of a spin-1/2 and a spin-j particle can lead to a lower local temperature compared to a refrigerator with two identical spin-j particles following the XYZ interactions.