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Physical Review A

Microwave-enhanced quantum heat engines via electromagnetically induced transparency

Xiaojun Zhang, Zi-Hao Shi, Hai-Hua Wang, Zhi‐Hui Kang, Jin-Hui Wu

Published Mar 8, 2019• 4 citations
Publisher

Abstract

Quantum heat engines based on electromagnetically induced transparency first proposed by Harris [S. E. Harris, Phys. Rev. A 94, 053859 (2016)] have been recently demonstrated in experiment. Here we present an improved version of such a heat engine by adding a microwave field in the $\mathrm{\ensuremath{\Lambda}}$-type atomic system to modify the cross sections for absorption and emission. We find that this microwave-assisted atomic system behaves as a heat engine only when (i) all three laser or microwave fields resonate with their corresponding transitions and (ii) the relative phase between these fields is $n\ensuremath{\pi}$ with $n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2,\ensuremath{\cdots}$. In particular, below the threshold of lasing without inversion, the engine's output field exhibits a brightness increasing with the microwave's intensity, and the brightness in the presence of a weak microwave field can be tens of (or even larger) that in the absence of a microwave field. We also note that the microwave field has the equivalent effect of increasing (decreasing) the hot (cold) reservoir's temperature.

DOI
10.1103/physreva.99.033817

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Quantum heat engines based on electromagnetically induced transparency first proposed by Harris [S. E. Harris, Phys. Rev. A 94, 053859 (2016)] have been recently demonstrated in experiment. Here we present an improved version of such a heat engine by adding a microwave field in the \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-type atomic system to modify the cross sections for absorption and emission. We find that this microwave-assisted atomic system behaves as a heat engine only when (i) all three laser or microwave fields resonate with their corresponding transitions and (ii) the relative phase between these fields is n\ensuremathπn\ensuremath{\pi}n\ensuremathπ with n=0,\ifmmode±\else\textpm\fi1,\ifmmode±\else\textpm\fi2,\ensuremath⋯n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2,\ensuremath{\cdots}n=0,\ifmmode±\else\textpm\fi1,\ifmmode±\else\textpm\fi2,\ensuremath⋯. In particular, below the threshold of lasing without inversion, the engine's output field exhibits a brightness increasing with the microwave's intensity, and the brightness in the presence of a weak microwave field can be tens of (or even larger) that in the absence of a microwave field. We also note that the microwave field has the equivalent effect of increasing (decreasing) the hot (cold) reservoir's temperature.
The single-atom version of the quantum heat engine based on electromagnetically induced transparency is theoretically investigated in this paper. In contact with a hot and a cold bath, the atom trapped in an optical cavity is coherently coupled by a coherent field, thus generating photons as output through a process that mimics a heat engine. Using semiclassical theory, we obtain the conditions for the classical gain parameter being positive. Then by taking a full quantum approach, we discuss the statistical property of the generated photons depicted by the photon number distribution and Wigner function, and show that it can be effectively tuned by the coupling field. Investigations on the energy and entropy balances of the heat engine process lead to an interesting result that the power of the engine is simply the energy per time provided by the hot reservoir. The coupling field plays a critical role in supporting the heat-engine process. However, the energy that it provides is all dumped into the cold reservoir. The total energy exchange conforms to the first law of thermodynamics. The efficiency of the engine depends on the temperatures of the two reservoirs and the strength of the coupling field. The entropy change of the heat-engine process suggests that when working far above the threshold of lasing, the efficiency approaches that of its atomic-ensemble-based partner.
Abstract This paper introduces a quantum heat engine model that utilizes an ultracold atomic gas coupled with a nanomechanical mirror. The mirror’s vibration induces an opto-mechanical sideband in the control field, affecting the behavior of the cold gas and subsequently influencing the output radiation of the engine. The model incorporates mirror vibration while omitting cavity confinement, establishing a bridge between a multi-level atom–laser interacting system that plays with coherences and the mechanical vibration of the nanomechanical mirror, which jointly function as heat engines. Three distinct heat engine configurations are proposed: the first involves a vibration-free three-level Λ-type system, the second introduces nanomechanical vibration to the three-level Λ-type system, and the third constitutes a composite engine that combines the previous setups along with nanomechanical vibration. The spectral brightness of a three-level heat engine is diminished with mirror vibration, whereas for a composite heat engine, there is a slight enhancement in the brightness peak. However, the maximum brightness is attained when there is no vibration. Comparisons between the proposed model and an ideal system are made regarding entropy balance, adhering to the constraints of the second law of thermodynamics. The model observed that when subjected to mirror vibration, the proposed heat engines diverged from the characteristics expected in an ideal heat engine.
In contact with a hot and a cold reservoir, the three-level atom driven by a strong coupling field generates photons via a sequence of transitions that mimics the running process of a heat engine. The brightness of the output photon can be much larger than that of the hot reservoir, and its efficiency could be larger than that of the Carnot engine [ Phys. Rev. A 94 , 053859 ( 2016 ) PLRAAN 1050-2947 10.1103/PhysRevA.94.053859 ]. The core element of the mechanism is an interference effect called electromagnetically induced transparency caused by the coupling field, which is commonly a perfect laser without any random change in the phase. In this paper, we investigate a more realistic model where the temporal fluctuation of the coupling field is considered. By applying the laws of thermodynamics in the analysis, we find that in addition to the reduced power of the engine, a relatively strong fluctuation changes the properties of the system radically, even making it lose the quality of being a heat engine. We have found the corresponding criteria for the maximal allowed fluctuation. The entropy changes when the engine works below the laser threshold suggest that the effect of the fluctuation is equivalent to increasing the temperature of the cold reservoir.
We study the statistics of the lasing output from a single-atom quantum heat engine, which was originally proposed by Scovil and Schulz-DuBois [H. E. D. Scovil and E. O. Schulz-DuBois, Phys. Rev. Lett. 2, 262 (1959)]. In this heat engine model, a single three-level atom is coupled with an optical cavity and is in contact with a hot and a cold heat bath together. We derive a fully quantum laser equation for this heat engine model and obtain the photon number distribution both below and above the lasing threshold. With the increase of the hot bath temperature, the population is inverted and lasing light comes out. However, we notice that if the hot bath temperature keeps increasing, the atomic decay rate is also enhanced, which weakens the lasing gain. As a result, another critical point appears at a very high temperature of the hot bath, after which the output light become thermal radiation again. To avoid this double-threshold behavior, we introduce a four-level heat engine model, where the atomic decay rate does not depend on the hot bath temperature. In this case, the lasing threshold is much easier to achieve and the double-threshold behavior disappears.