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arXiv:2412.10472 · Physical review. E

Quantum evolution of mixed states and performance of quantum heat engines

Anatoly A. Svidzinsky, Wenzhuo Zhang

Published Apr 8, 2026• 0 citations

Abstract

We introduce a technique for calculating the density operator time evolution along the lines of Heisenberg representation of quantum mechanics. Using this technique, we find the exact solution for the evolution of two and three coupled harmonic oscillators initially prepared in thermal states at different temperatures. We show that such systems exhibit interesting quantum dynamics in which oscillators swap their thermal states due to correlation induced in the process of energy exchange and yield noise-induced coherence. A photonic quantum heat engine (QHE) composed of two optical cavities can be modeled as coupled harmonic oscillators with time-dependent frequencies. Photons in the cavities become correlated during the engine operation. We show that the work done by such an engine is maximum if at the end of the cycle the oscillators swap numbers of excitations which can be achieved when the engine operates under the condition of parametric resonance. We also show that Carnot formula yields limiting efficiency for QHEs under general assumptions. Moreover, we show that, by making a canonical transformation, density operator of arbitrary n-mode Gaussian state can be written as a product of n thermal density operators describing independent collective excitations with different temperatures. Thus, operation of QHEs based on the correlated Gaussian states is equivalent to that based on uncorrelated thermal reservoirs. Our results deepen understanding of quantum evolution of mixed states which could be useful to design quantum machines with better performance.

DOI: 10.1103/v5bc-p2mw

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\mathrm{EMP}

) is examined. In accordance with earlier theoretical predictions, to leading order, we find that $\mathrm{EMP}\ensuremath{\sim}{\ensuremath{\eta}}_{c}/2$, where ${\ensuremath{\eta}}_{c}$ is Carnot efficiency. However, the next higher order coefficient is system dependent and hence nonuniversal.

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Abstract Entangled states are an important resource for quantum information processing and for the fundamental understanding of quantum physics. An intriguing open question would be whether entanglement can improve the performance of quantum heat engines in particular. One of the promising platforms to address this question is to use entangled atoms as a non-thermal bath for cavity photons, where the cavity mirror serves as a piston of the engine. Here we theoretically investigate a photonic quantum engine operating under an effective reservoir consisting of quantum-correlated pairs of atoms. We find that maximally entangled Bell states alone do not help extract useful work from the reservoir unless some extra populations in the excited states or ground states are taken into account. Furthermore, high efficiency and work output are shown for the non-maximally entangled superradiant state, while negligible for the subradiant state due to lack of emitted photons inside the cavity. Our results provide insights in the role of quantum-correlated atoms in a photonic engine and present new opportunities in designing a better quantum heat engine.