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Physical Review Applied

Coherence-Induced Reversibility and Collective Operation of Quantum Heat Machines via Coherence Recycling

Raam Uzdin

Published Aug 8, 2016• 107 citations
Publisher

Abstract

In $c\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e$ $o\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}s$, units interact to generate synergistic effects beyond what the individual, noninteracting units could yield. A quantum collective with no classical analogue is even more intriguing. In the context of quantum thermodynamics, the authors use the concept of extracting and injecting $c\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}e$ to envision a collective heat machine of the same efficiency as its individual engines, yet drawing more heat from thermal baths and producing more work, its power scaling quadratically with the number of engines. Surprisingly, the collective machine can be more reversible than its most reversible element.

DOI
10.1103/physrevapplied.6.024004

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In c\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e o\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}s, units interact to generate synergistic effects beyond what the individual, noninteracting units could yield. A quantum collective with no classical analogue is even more intriguing. In the context of quantum thermodynamics, the authors use the concept of extracting and injecting c\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}e to envision a collective heat machine of the same efficiency as its individual engines, yet drawing more heat from thermal baths and producing more work, its power scaling quadratically with the number of engines. Surprisingly, the collective machine can be more reversible than its most reversible element.
Abstract When quantum heat engines or refrigerators operate in the over-thermalization regime, quantum effects are not expected as the thermal baths eliminates all coherences. In this work we show that even in this seemingly non-quantum regime, it is possible to harvest coherence before it is erased, and obtain non classical effects. While the engine is not affected by the coherence harvesting, the extracted coherence can be used to cool external particles and reduce their entropy (the energy of the auxiliary particles is not modified). On top of cooling the extracted coherence can activate passive states. Coherence extraction also has an impact on the basic theory of heat machines. With coherence extraction, the standard expression for the total entropy production -Qc/Tc-Qh/Th is replaced by a simple relative entropy expression, that is orders of magnitude smaller in the regime of interest. Consequently, coherence extraction enables reversibility that is otherwise impossible. In addition, we present a collective engine operation scheme where coherence is recycled and shared between engines. This leads to an interesting performance boost where the total power scales quadratically with the number of engines, rather than linearly. Finally, a scheme for resource accounting is presented. It is demonstrated that coherence extraction and coherence injection extend the scope of known quantum thermal machines and add new modes of operation.
Collective behavior where a set of elements interact and generate effects that are beyond the reach of the individual non interacting elements, are always of great interest in physics. Quantum collective effects that have no classical analogue are even more intriguing. In this work we show how to construct collective quantum heat machines and explore their performance boosts with respect to regular machines. Without interactions between the machines the individual units operate in a stochastic, non-quantum manner. The construction of the collective machine becomes possible by introducing two simple quantum operations: coherence extraction and coherence injection. Together these operations can harvest coherence from one engine and use it to boost the performance of a slightly different engine. For weakly driven engines we show that the collective work output scales quadratically with the number of engines rather than linearly. Eventually, the boost saturates and the scaling becomes linear. Nevertheless, even in saturation, work is still significantly boosted compared to individual operation. To study the reversibility of the collective machine we introduce the 'entropy pollution' measure. It is shown that there is a regime where the collective machine is N times more reversible while producing N times more work, compared to the individual operation of N units. Moreover, the collective machine can even be more reversible than the most reversible unit in the collective. This high level of reversibility becomes possible due to a special symbiotic mechanism between engine pairs.
The interplay between quantum-mechanical properties, such as coherence, and classical notions, such as energy, is a subtle topic at the forefront of quantum thermodynamics. The traditional Carnot argument limits the conversion of heat to work; here we critically assess the problem of converting coherence to work. Through a careful account of all resources involved in the thermodynamic transformations within a fully quantum-mechanical treatment, we show that there exist thermal machines extracting work from coherence arbitrarily well. Such machines only need to act on individual copies of a state and can be reused. On the other hand, we show that for any thermal machine with finite resources not all the coherence of a state can be extracted as work. However, even bounded thermal machines can be reused infinitely many times in the process of work extraction from coherence.
Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study both from a fundamental perspective and in view of applications. One essential question is whether collective effects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is, its performance, but, additionally, its constancy, that is, the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency, and constancy scale with the number of spins composing the engine and introduce a well-defined macroscopic limit where analytical expressions are obtained. Our results predict power enhancements, in both finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, accompanied by coherence-enhanced constancy for finite sizes. We discuss these quantities in connection to thermodynamic uncertainty relations.
Abstract The introduction of the quantum analogue of a Carnot engine based on a bath comprising of particles with a small amount of coherence initiated an active line of research on the harnessing of different quantum resources for the enhancement of thermal machines beyond the standard reversible limit, with an emphasis on non-thermal baths containing quantum coherence. In our work, we investigate the impact of coherence on the thermodynamic tasks of a collision model which is composed of a system interacting, in the continuous time limit, with a series of coherent ancillas of two baths at different temperatures. Our results show the advantages of utilising coherence as a resource in the operation of the machine, and allows it: (a) to exhibit unconventional behaviour such as the appearance of a hybrid refrigerator, capable of simultaneous refrigeration and generation of work, and (b) to function as an engine or a refrigerator with efficiencies larger than the Carnot bound. Moreover, we find an effective upper bound to the efficiency of the thermal machine operating as an engine in the presence of a coherent reservoir.