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arXiv:1811.02917 · Physical Review Letters

Efficiency of a Quantum Otto Heat Engine Operating under a Reservoir at Effective Negative Temperatures

Rogério J. de Assis, Taysa Mendes de Mendonça, Celso J. Villas-Bôas, Alexandre M. Souza, Roberto S. Sarthour, Ivan S. Oliveira, N. G. de Almeida

Published Jun 19, 2019• 147 citations
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Abstract

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.

DOI
10.1103/physrevlett.122.240602

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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.
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.
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We consider the efficiency at maximum power of a quantum Otto engine, which uses a spin or a harmonic system as its working substance and works between two heat reservoirs at constant temperatures Th{T}_{h}Th​ and Tc{T}_{c}Tc​ (<Th)(<{T}_{h})(<Th​). Although the behavior of spin-1/21/21/2 system differs substantially from that of the harmonic system in that they obey two typical quantum statistics, the efficiencies at maximum power based on these two different kinds of quantum systems are bounded from the upper side by the same expression ${\ensuremath{\eta}}_{\mathrm{mp}}\ensuremath{\le}{\ensuremath{\eta}}_{+}\ensuremath{\equiv}{\ensuremath{\eta}}_{C}^{2}/[{\ensuremath{\eta}}_{C}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C})ln(1\ensuremath{-}{\ensuremath{\eta}}_{C})]$ with ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$ as the Carnot efficiency. This expression ${\ensuremath{\eta}}_{\mathrm{mp}}$ possesses the same universality of the CA efficiency ${\ensuremath{\eta}}_{\mathrm{CA}}=1\ensuremath{-}\sqrt{1\ensuremath{-}{\ensuremath{\eta}}_{C}}$ at small relative temperature difference. Within the context of irreversible thermodynamics, we calculate the Onsager coefficients and show that the value of ${\ensuremath{\eta}}_{\mathrm{CA}}$ is indeed the upper bound of EMP for an Otto engine working in the linear-response regime.
Abstract Recent theoretical and experimental studies in quantum heat engines show that, in the quasi-static regime, it is possible to have higher efficiency than the limit imposed by Carnot, provided that engineered reservoirs are used. The quasi-static regime, however, is a strong limitation to the operation of heat engines, since an infinitely long time is required to complete a cycle. In this paper we propose a two-level model as the working substance to perform a quantum Otto heat engine surrounded by a cold thermal reservoir and a squeezed hot thermal reservoir. Taking advantage of this model we show a striking achievement, that is to attain unity efficiency even at non-null power.
We study quantum Otto thermal machines with a two-spin working system coupled by anisotropic interaction. Depending on the choice of different parameters, the quantum Otto cycle can function as different thermal machines, including a heat engine, refrigerator, accelerator, and heater. We aim to investigate how the anisotropy plays a fundamental role in the performance of the quantum Otto engine (QOE) operating in different timescales. We find that while the engine's efficiency increases with the increase in anisotropy for the quasistatic operation, quantum internal friction and incomplete thermalization degrade the performance in a finite-time cycle. Further, we study the quantum heat engine (QHE) with one of the spins (local spin) as the working system. We show that the efficiency of such an engine can surpass the standard quantum Otto limit, along with maximum power, thanks to the anisotropy. This can be attributed to quantum interference effects. We demonstrate that the enhanced performance of a local-spin QHE originates from the same interference effects, as in a measurement-based QOE for their finite-time operation.