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Entropy Production and Efficiency Enhancement in Quantum Otto Engines Operating at Negative Temperature

Aryadine F. de Sousa, Gabriella G. Damas, N. G. de Almeida

Published Jan 1, 2024• 1 citation
Publisher
DOI
10.2139/ssrn.4868781

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Cyclic classical and quantum thermal machines show higher efficiency when the strokes are carried out quasi-statically. Recent theoretical and experimental work on figures of merit for thermal machines show that they have an advantage when operating in environments with negative temperatures. In an experimental proof of concept [Phys. Rev. Lett. 122, 240602 (2019)], it was shown that quantum Otto engines operating at negative temperatures can exhibit a behavior in which the faster the cycle is carried out, the higher the efficiency. In this work, we make use of the concept of entropy production and friction work to explain this counterintuitive behavior, and we show that it only occurs when reservoirs have negative temperatures.

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Cyclic classical and quantum thermal machines show higher efficiency when the strokes are carried out quasi-statically. Recent theoretical and experimental work on figures of merit for thermal machines show that they have an advantage when operating in environments with negative temperatures. In an experimental proof of concept [Phys. Rev. Lett. 122, 240602 (2019)], it was shown that quantum Otto engines operating at negative temperatures can exhibit a behavior in which the faster the cycle is carried out, the higher the efficiency. In this work, we make use of the concept of entropy production and friction work to explain this counterintuitive behavior, and we show that it only occurs when reservoirs have negative temperatures.
Heat engines usually operate by exchanging heat with thermal baths at different (positive) temperatures. Nonthermal baths may, however, lead to a significant performance boost. We here experimentally analyze the power output of a single-atom quantum Otto engine realized in the quasi-spin states of individual Cesium atoms interacting with an atomic Rubidium bath. From measured time-resolved populations of the quasi-spin state, we determine the dynamics during the cycle of both the effective spin temperature and of the quantum fluctuations of the engine, which we quantify with the help of the Shannon entropy. We find that power is enhanced in the negative temperature regime, and that it reaches its maximum value at half the maximum entropy. Quantitatively, operating our engine at negative effective temperatures increases the power by up to 30% compared to operation at positive temperatures, including even the case of infinite temperature. At the same time, entering the negative temperature regime allows for reducing the entropy to values close to zero, offering highly stable operation at high power output. We furthermore numerically investigate the influence of the size of the Hilbert space on the performance of the quantum engine by varying the number of levels of the working medium. Our work thereby paves the way to fluctuation control in the operation of high-power and efficient single-atom quantum engines.