Algebraic approach to a two-qubit quantum thermal machine

TL;DR

This paper employs algebraic methods to analyze a two-qubit quantum Otto engine, exploring its thermodynamic performance, efficiency, and operation regimes under various temperature and frequency settings.

Contribution

It introduces an algebraic approach to study a two-qubit quantum thermal machine with time-dependent parameters, providing new insights into its efficiency and operational regimes.

Findings

Engine efficiency varies with Rabi frequency modulation.

Different temperature and frequency settings lead to distinct operation regimes.

Algebraic methods effectively analyze time-dependent quantum thermal systems.

Abstract

Algebraic methods for solving time dependent Hamiltonians are used to investigate the performance of quantum thermal machines. We investigate the thermodynamic properties of an engine formed by two coupled q-bits, performing an Otto cycle. The thermal interaction occurs with two baths at different temperatures, while work is associated with the interaction with an arbitrary time-dependent magnetic field that varies in intensity and direction. For the coupling, we consider the 1-d isotropic Heisenberg model, which allows us to describe the system by means of the irreducible representation of the $\mathfrak{su}(2)$ Lie algebra within the triplet subspace. We inspect different settings of the temperatures and frequencies of the cycle and investigate the corresponding operation regimes of the engine. Finally, we numerically investigate the engine efficiency under a time varying Rabi frequency, interpolating the abrupt and adiabatic limits.