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Science

Coherent Power Booster

Heiner Linke

Published Feb 7, 2003• 4 citations
Publisher

Abstract

According to the Second Law of Thermodynamics, a heat engine requires two heat baths to operate-a warm source of heat and a cooler dump for waste heat. In apparent violation of this law, Scully et al. propose a heat engine that uses quantum coherence to extract work from a single, warm gas. In his Perspective, Linke explains that the Second Law is not violated, because the power extracted from the bath is smaller than that required to achieve coherence. By combining quantum mechanics with traditional heat engines, the efficiencies of various kinds of motors could be enhanced.

DOI
10.1126/science.1080886

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According to the Second Law of Thermodynamics, a heat engine requires two heat baths to operate-a warm source of heat and a cooler dump for waste heat. In apparent violation of this law,
Scully
et al. propose a heat engine that uses quantum coherence to extract work from a single, warm gas. In his Perspective,
Linke
explains that the Second Law is not violated, because the power extracted from the bath is smaller than that required to achieve coherence. By combining quantum mechanics with traditional heat engines, the efficiencies of various kinds of motors could be enhanced.
We consider a quantum engine driven by repeated weak interactions with a heat bath of identical three-level atoms. This model was first introduced by Scully et al. [Science 299, 862 (2003)SCIEAS0036-807510.1126/science.1078955], who showed that coherence between the energy-degenerate ground states serves as a thermodynamic resource that allows operation of a thermal cycle with a coherence-dependent thermalization temperature. We consider a similar engine out of the quasistatic limit and find that the ground-state coherence also determines the rate of thermalization, therefore increasing the output power and the engine efficiency only when the thermalization temperature is reduced; revealing a more nuanced perspective of coherence as a resource. This allows us to optimize the output power by adjusting the coherence and relative stroke durations.
We present here a quantum Carnot engine in which the atoms in the heat bath are given a small bit of quantum coherence. The induced quantum coherence becomes vanishingly small in the high-temperature limit at which we operate and the heat bath is essentially thermal. However, the phase phi, associated with the atomic coherence, provides a new control parameter that can be varied to increase the temperature of the radiation field and to extract work from a single heat bath. The deep physics behind the second law of thermodynamics is not violated; nevertheless, the quantum Carnot engine has certain features that are not possible in a classical engine.
The question of whether quantum coherence is a resource beneficial or detrimental to the performance of quantum heat engines has been thoroughly studied but remains undecided. To isolate the contribution of coherence, we analyze the performance of a purely coherence-driven quantum heat engine, a device that does not include any heat flow during the thermodynamic cycle. The engine is powered by the coherence of a multiqubit system, where each qubit is charged via interaction with a coherence bath using the Jaynes-Cummings model. We demonstrate that optimal coherence charging and hence extractable work is achieved when the coherence bath has an intermediate degree of coherence. In our model, the extractable work is maximized when four copies of the charged qubits are used. Meanwhile, the efficiency of the engine, given by the extractable work per input coherence flow, is optimized by avoiding the coherence being stored in the system-bath correlations that is inaccessible to work. We numerically find that the highest efficiency is obtained for slightly lower temperatures and weaker system-bath coupling than those for optimal coherence charging.
With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's demon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.