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Journal of Physics A Mathematical and Theoretical

The effects of common reservoirs on the performance of a quantum refrigerator

Yue Liu, Wei‐Bin Yan, Yun‐Jie Xia, Zhong‐Xiao Man

Published Jun 20, 2024• 1 citation
Publisher

Abstract

Abstract In this work, we study and find that the performance of an autonomous refrigerator can be improved by means of collective dissipations of common reservoirs. The refrigerator is based on a four-level system with two degenerate levels, coupled to three thermal reservoirs with different temperatures. Our study reveals that utilizing only one common reservoir can not significantly enhance the refrigerator’s performance. However, when two reservoirs are shared simultaneously, the performance improvement becomes more evident. Furthermore, we find that the refrigerator’s performance can be further enhanced by operating in a regime where the decoherence-free subspace is present. Our results indicate that careful engineering is essential to maximize the benefits of common reservoirs in enhancing the performance of quantum thermal machines.

DOI
10.1088/1751-8121/ad5a56

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Abstract In this work, we study and find that the performance of an autonomous refrigerator can be improved by means of collective dissipations of common reservoirs. The refrigerator is based on a four-level system with two degenerate levels, coupled to three thermal reservoirs with different temperatures. Our study reveals that utilizing only one common reservoir can not significantly enhance the refrigerator’s performance. However, when two reservoirs are shared simultaneously, the performance improvement becomes more evident. Furthermore, we find that the refrigerator’s performance can be further enhanced by operating in a regime where the decoherence-free subspace is present. Our results indicate that careful engineering is essential to maximize the benefits of common reservoirs in enhancing the performance of quantum thermal machines.
We study the effects of common reservoirs on the performance of an autonomous three-level quantum refrigerator. We show that the common reservoirs can result not only in additional transitions but also different types of interferences between them. For the case that the sole object to be cooled is a cold reservoir, it turns out that the cooling power can be greatly enhanced by the common reservoirs as well as by the induced interference. For the configuration that the refrigerator acts on both the cold reservoir and a qubit, we find that though the common reservoirs can improve the cooling power, which instead is detrimental to the cooling of the qubit. The interference also manifests different effects on the cooling of the cold reservoir and the qubit. Our results provide an evidence of possibility on applying the common reservoirs to enhance the performance of the refrigerator.
Abstract We explore the possibility of enhancing the performance of small thermal machines by the presence of common noise sources. In particular, we study a prototypical model for an autonomous quantum refrigerator comprised by three qubits coupled to thermal reservoirs at different temperatures. Our results show that engineering the coupling to the reservoirs to act as common environments lead to relevant improvements in the performance. The enhancements arrive to almost double the cooling power of the original fridge without compromising its efficiency. The greater enhancements are obtained when the refrigerator may benefit from the presence of a decoherence-free subspace. The influence of coherent effects in the dissipation due to one- and two-spin correlated processes is also examined by comparison with an equivalent incoherent yet correlated model of dissipation.
Abstract We propose a model of two identical autonomous quantum refrigerators that interact through their qubits coupled to cold thermal baths. We consider the same specific disposition for each refrigerator related to a three-level system coupled to different thermal baths and, in turn, to a qubit as the object to be cooled. By coupling the two systems, we show that under certain conditions on the model parameters, the devices can operate in the regime of an independent autonomous quantum refrigerator or be subject to an adjustment of the thermodynamic performances. We further investigate the correlations induced by the interaction between the two refrigerators, and illustrate their behavior with respect to their thermodynamic performances. We have found that adjusting the different interaction constants of the model can lead to an evolution of the quantum correlations of the two machines that is inversely related to the behavior of the thermodynamic quantities of both refrigerators. However, this is not necessarily the case when the temperatures of the model are considered as the reference parameters.
Quantum coherence has been shown to impact the operational capabilities of quantum systems performing thermodynamic tasks in a significant way, and yet the possibility and conditions for genuine coherence-enhanced thermodynamic operation remain unclear. Introducing a comparison with classical machines using the same set of thermodynamic resources, we show that for steady-state quantum thermal machines – both autonomous and externally driven – that interact weakly with thermal reservoirs and work sources, the presence of coherence induced by perturbations in the machine Hamiltonian guarantees a genuine thermodynamic advantage under mild conditions. This advantage applies to both cases where the induced coherence is between levels with different energies or between degenerate levels. On the other hand, we show that engines subjected to noise-induced coherence can be outperformed by classical stochastic engines using exactly the same set of (incoherent) resources. We illustrate our results with three prototypical models of heat engines and refrigerators: the three-level amplifier, the three-qubit autonomous refrigerator, and a noise-induced-coherence machine.
Absorption refrigerators transfer thermal energy from a cold reservoir to a hot reservoir using input energy from a third, so-called work reservoir. We examine the operation of quantum absorption refrigerators when coherences between eigenstates survive in the steady state limit. In our model, the working medium comprises a discrete, four-level system. Several studies on related setups have demonstrated the performance-enhancing potential of steady-state eigenbasis quantum coherences. By contrast, in our model such coherences generally quench the cooling current in the refrigerator, while minimally affecting the coefficient of performance (cooling efficiency). We rationalize the behavior of the four-level refrigerator by studying three-level model systems for energy transport and refrigeration. Our calculations further illuminate the shortcomings of secular quantum master equations and the necessity of employing dynamical equations of motion that retain couplings between population and coherences.
The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But is this connection always an evidence of "quantum-thermodynamic supremacy"? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level continuous quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot and it may exhibit a larger cooling rate and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any N-level weakly driven device with a "cyclic" pattern of transitions. Therefore, even if coherence is present in a specific quantum thermal machine, it is often not essential to replicate the underlying energy conversion process.