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arXiv:1305.6009 · Physical Review E

Entanglement enhances cooling in microscopic quantum refrigerators

Nicolas Brunner, Marcus Huber, Noah Linden, Sandu Popescu, Ralph Silva, Paul Skrzypczyk

Published Mar 13, 2014• 219 citations
arXivHTMLPDF

Abstract

Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned-fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.

DOI
10.1103/physreve.89.032115

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Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned-fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.
Understanding the thermodynamics of quantum systems is of fundamental importance, from both theoretical and experimental perspectives. A growing interest has been recently given to small self-contained quantum thermal machines, the functioning of which requires no external source of work or control, but only incoherent interactions with thermal baths. The simplicity of such machines makes them and ideal test-bed for exploring quantum thermodynamics. So far, however, the importance of quantum effects in these machines has remained elusive. Here we show that entanglement, the paradigmatical quantum effect, plays a fundamental role in small self-contained quantum refrigerators, as it can enhance cooling and energy transport -- except notably when the efficiency is close to the Carnot limit. Hence a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling. More generally, our work shows that entanglement opens new possibilities in thermodynamics.
An implementation of quantum absorption chillers with three qubits has been recently proposed that is ideally able to reach the Carnot performance regime. Here we study the working efficiency of such self-contained refrigerators, adopting a consistent treatment of dissipation effects. We demonstrate that the coefficient of performance at maximum cooling power is upper bounded by 3/4 of the Carnot performance. The result is independent of the details of the system and the equilibrium temperatures of the external baths. We provide design prescriptions that saturate the bound in the limit of a large difference between the operating temperatures. Our study suggests that delocalized dissipation, which must be taken into account for a proper modeling of the machine-baths interaction, is a fundamental source of irreversibility which prevents the refrigerator from approaching the Carnot performance arbitrarily closely in practice. The potential role of quantum correlations in the operation of these machines is also investigated.
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A small quantum absorption refrigerator, consisting of three qubits, is discussed in the transient regime. We discuss time scales for coherent dynamics, damping, and approach to the steady state, and we study cooling and entanglement. We observe that cooling can be enhanced in the transient regime, in the sense that lower temperatures can be achieved compared to the steady-state regime. This is a consequence of coherent dynamics but can occur even when this dynamics is strongly damped by the dissipative thermal environment, and we note that precise control over couplings or timing is not needed to achieve enhanced cooling. We also show that the amount of entanglement present in the refrigerator can be much larger in the transient regime compared to the steady state. These results are of relevance to future implementations of quantum thermal machines.
Small quantum absorption refrigerators have recently attracted renewed attention. Here we present a missing design of a two-qubit fridge, the main feature of which is that one of the two machine qubits is itself maintained at a temperature colder than the cold bath. This is achieved by "reversing" the couplings to the baths compared to previous designs, where only a transition is maintained cold. We characterize the working regime and the efficiency of the fridge. We demonstrate the soundness of the model by deriving and solving a master equation. Finally, we discuss the performance of the fridge, in particular the heat current extracted from the cold bath. We show that our model performs comparably to the standard three-level quantum fridge and thus appears appealing for possible implementations of nanoscale thermal machines.
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.