We examine a quantum Otto engine using both Bose–Einstein condensation (BEC) and normal Bose gas as working medium trapped in generalized external potential. We treated the engine quasi-statically and endoreversibly. Since the expansion and compression in both quasi-static and endoreversible take place isentropic, the expression of efficiency is similar. However, the power output in the quasi-static cycle is zero due to infinite and long stroke time. In contrast, with an endoreversible cycle, thermalization with two reservoirs takes place at a finite time. We use Fourier’s law of conduction to formulate the relation between temperature of medium and reservoir, making work depend on heating and cooling stroke time. Moreover, we maximized the power with respect to compression ratio \(\kappa\) to obtain efficiency at maximum power (EMP). We found that EMP is significantly higher when using BEC as a working medium; meanwhile, EMP with normal Bose gas is just Curzon–Ahlborn efficiency. We also investigate the effect of thermal contact time \(\tau\) with hot \((\tau _{h})\) and cold \((\tau _{l})\) reservoir on EMP. We found that when complete thermalization, \(\tau _{h}=\tau _{l}\), stroke time occurs, there are no significant differences. Nevertheless, while incomplete thermalization arises, adjusting various cooling and heating stroke time provides a significant result on EMP, which is much higher at \(\tau _{h}<\tau _{l}\) stroke time and lower at \(\tau _{h}>\tau _{l}\) stroke time. We conclude this incomplete thermalization leads to the condition where residual coherence emerges which enhances the EMP of the engine.

我们使用玻色-爱因斯坦凝聚（BEC）和普通玻色气体作为工作介质来研究量子奥托发动机，该发动机被困在广义外部电势中。我们对发动机进行了准静态和内可逆处理。由于准静态和内可逆的膨胀和压缩都是等熵的，因此效率的表达式是相似的。然而，由于冲程时间无限长，准静态循环中的功率输出为零。相比之下，对于内可逆循环，两个储层的热化发生在有限的时间内。我们利用傅里叶传导定律来制定介质温度和储液器温度之间的关系，使功取决于加热和冷却冲程时间。此外，我们根据压缩比\(\kappa\)最大化功率，以获得最大功率 (EMP) 下的效率。我们发现使用BEC作为工作介质时EMP明显更高；同时，普通玻色气体的电磁脉冲只是柯松-阿尔伯恩效率。我们还研究了热\ ((\tau _{h})\)和冷\((\tau _{l})\)储层的热接触时间\(\tau\)对电磁脉冲的影响。我们发现，当完全热化时，\(\tau _{h}=\tau _{l}\)发生冲程时间，没有显着差异。然而，虽然出现不完全热化，但调整各种冷却和加热冲程时间对 EMP 提供了显着的结果，在\(\tau _{h}<\tau _{l}\)冲程时间处要高得多，而在\( \tau _{h}>\tau _{l}\)冲程时间。我们得出的结论是，这种不完全热化会导致出现残余相干性，从而增强发动机的电磁脉冲。