受监测的非绝热与相干控制的量子幺正 Otto 热机：前四阶累积量
Monitored non-adiabatic and coherent-controlled quantum unital Otto heat engines: First four cumulants
AI总结：
本文研究了单自旋-1/2量子Otto热机，通过引入任意幺正信道和监测机制，推导出功和热的前四阶累积量解析表达式，揭示了非对称驱动下正功的必要条件及高阶累积量比值的无界性，并探讨了相干控制对热机性能的影响。
摘要：
最近，基于测量的量子热机在量子热力学领域引起了更多关注。然而，先前关于量子 Otto 热机的结果要么局限于浴阶段特殊的幺正和非幺正信道，要么局限于做功冲程的特定驱动协议，并假设循环是时间反转对称的，即 $V^{\dagger}=U$（或 $V=U$）。在本文中，我们考虑一个单自旋-1/2 量子 Otto 热机，首先将其中一个热浴替换为任意的幺正信道，然后给出了特征函数的精确解析表达式，功和热的所有累积量均可从中得出。我们证明，在监测的作用下，无论对于对称还是非对称驱动的 Otto 循环，$ν_{2}>ν_{1}$ 都是产生正功的必要条件。此外，超越平均值，我们证明了当系统作为热机工作时，功和热涨落的比值具有下界和上界。然而，与文献中已有的结果不同，我们还考虑了第三和第四阶累积量。结果表明，功和热的第三（四）阶累积量之比既不以 1 为上界，也不以效率的第三（四）次方为下界，这与涨落比值的情况不同。最后，我们考虑应用一个特定的幺正映射，它以相干叠加的方式扮演热浴的角色，并展示了控制量子比特的初始相干性对效率、平均功及其相对涨落的影响。
英文摘要：
Recently, measurement-based quantum thermal machines have drawn more attention in the field of quantum thermodynamics. However, the previous results on quantum Otto heat engines were either limited to special unital and non-unital channels in the bath stages, or a specific driving protocol at the work strokes and assuming the cycle being time-reversal symmetric i.e. $V^{\dagger}=U$ (or $V=U$). In this paper, we consider a single spin-1/2 quantum Otto heat engine, by first replacing one of the heat baths by an arbitrary unital channel and then we give the exact analytical expression of the characteristic function from which all the cumulants of heat and work emerge. We prove that under the effect of monitoring, $ν_{2}>ν_{1}$ is a necessary condition for positive work, either for a symmetric or asymmetric-driven Otto cycle. Furthermore, going beyond the average we show that the ratio of the fluctuations of work and heat is lower and upper-bounded when the system is working as a heat engine. However, differently from the previous results in the literature, we consider the third and fourth cumulants as well. It is shown that the ratio of the third (fourth) cumulants of work and heat is not upper-bounded by unity nor lower-bounded by the third (fourth) power of the efficiency, as is the case for the ratio of fluctuations. Finally, we consider applying a specific unital map that plays the role of a heat bath in a coherently superposed, manner and we show the role of the initial coherence of the control qubit on efficiency, on the average work and its relative fluctuations.
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