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Power of a Quasispin Quantum Otto Engine at Negative Effective Spin Temperature

Jens Nettersheim, Sabrina Burgardt, Quentin Bouton, Daniel Adam, Eric Lutz, Artur Widera

Published Dec 23, 2022• 23 citations
Publisher

Abstract

A negative-temperature quantum heat engine is experimentally implemented with a single Cs atom in an Rb bath, demonstrating how negative temperatures can both enhance the output power and reduce fluctuations in comparison to positive temperatures.
DOI
10.1103/prxquantum.3.040334

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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.
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.
We perform an experiment in which a quantum heat engine works under two reservoirs, one at a positive spin temperature and the other at an effective negative spin temperature, i.e., when the spin system presents population inversion. We show that the efficiency of this engine can be greater than that when both reservoirs are at positive temperatures. We also demonstrate the counterintuitive result that the Otto efficiency can be beaten only when the quantum engine is operating in the finite-time mode.
Quantum heat engines are subjected to quantum fluctuations related to their discrete energy spectra. Such fluctuations question the reliable operation of thermal machines in the quantum regime. Here, we realize an endoreversible quantum Otto cycle in the large quasi-spin states of Cesium impurities immersed in an ultracold Rubidium bath. Endoreversible machines are internally reversible and irreversible losses only occur via thermal contact. We employ quantum control to regulate the direction of heat transfer that occurs via inelastic spin-exchange collisions. We further use full-counting statistics of individual atoms to monitor quantized heat exchange between engine and bath at the level of single quanta, and additionally evaluate average and variance of the power output. We optimize the performance as well as the stability of the quantum heat engine, achieving high efficiency, large power output and small power output fluctuations.
Quantum heat engines are subjected to quantum fluctuations related to their discrete energy spectra. Such fluctuations question the reliable operation of thermal machines in the quantum regime. Here, we realize an endoreversible quantum Otto cycle in the large quasi-spin states of Cesium impurities immersed in an ultracold Rubidium bath. Endoreversible machines are internally reversible and irreversible losses only occur via thermal contact. We employ quantum control to regulate the direction of heat transfer that occurs via inelastic spin-exchange collisions. We further use full-counting statistics of individual atoms to monitor quantized heat exchange between engine and bath at the level of single quanta, and additionally evaluate average and variance of the power output. We optimize the performance as well as the stability of the quantum heat engine, achieving high efficiency, large power output and small power output fluctuations.
We consider the finite-time performance of a quantum Otto engine working between a hot squeezed and a cold thermal bath at inverse temperatures ${\ensuremath{\beta}}_{h}$ and ${\ensuremath{\beta}}_{c}(>{\ensuremath{\beta}}_{h})$ with $({k}_{B}\ensuremath{\equiv}1)\ensuremath{\beta}=1/T$. We derive the analytical expressions for work, efficiency, power, and power fluctuations, in which the squeezing parameter is involved. By optimizing the power output with respect to two frequencies, we derive the efficiency at maximum power as ${\ensuremath{\eta}}_{mp}={({\ensuremath{\eta}}_{C}^{\mathrm{gen}})}^{2}/[{\ensuremath{\eta}}_{C}^{\mathrm{gen}}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C}^{\mathrm{gen}})ln(1\ensuremath{-}{\ensuremath{\eta}}_{C}^{\mathrm{gen}})]$, where the generalized Carnot efficiency ${\ensuremath{\eta}}_{C}^{\mathrm{gen}}$ in the high-temperature or small squeezing limit simplifies to an analytic function of squeezing parameter $\ensuremath{\gamma}$: ${\ensuremath{\eta}}_{C}^{\mathrm{gen}}=1\ensuremath{-}{\ensuremath{\beta}}_{h}/[{\ensuremath{\beta}}_{c}cosh(2\ensuremath{\gamma})]$. Within the context of irreversible thermodynamics, we demonstrate that the expression of efficiency at maximum power satisfies a general form derived from nonlinear steady state heat engines. We show that, the power fluctuations are considerably increased, although the engine efficiency is enhanced by squeezing.