We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.

中文翻译：

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权衡品质因数下量子谐波奥托发动机和制冷机的性能分析


我们研究了在绝热和非绝热（突然切换）频率调制的品质因数权衡下量子奥托发动机和瞬态谐振子制冷循环的最佳性能。对于热机（冰箱），所选择的权衡品质因数是由效率（性能系数）和功输出（冷却负载）的乘积定义的目标函数，因此代表了它们之间的折衷。我们获得了谐波奥托循环的效率和性能系数的解析表达式，以实现热机在各种运行状态下的最佳性能。特别是，在突然切换状态下，我们讨论了非绝热驱动对所考虑的热机性能的影响，并获得了谐波奥托热机的最大可实现效率和性能系数的解析表达式。特别是，我们证明了由突然切换协议驱动的量子谐波奥托循环在低温极限下不能作为热机或制冷机工作。最后，我们表明，在高温极限下，摩擦效应会产生更丰富的谐波奥托循环相图结构。我们将奥托循环的运行参数确定为热机、制冷机、加速器和加热器。