In this work, we obtain an analytical representation of the density operator of an atom in a dissipative cavity when the reservoir is at zero temperature and the total number of excitations is N = 1. We also investigated the quantum speed limit time (QSLT) of the atom and the non-Markovianity in the dynamics process. The results show that the QSLT and the non-Markovianity can be effectively manipulated by the atom–cavity coupling and the reservoir parameters. Both of the atom–cavity coupling and the detuning can induce a sudden transition from Markovian to non-Markovian dynamics, and this transition is the main physical reason of the quantum speed-up process. The critical value of the sudden transition from no speed-up to speed-up the atom–cavity coupling and the reservoir parameters. The corresponding physical explanation is also provided for our results.

中文翻译：

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耗散腔中原子的量子加速过程

在这项工作中，当储层处于零温度且激发总数为N = 1时，我们获得了耗散腔中原子的密度算符的解析表示。我们还研究了量子速度限制时间（QSLT）动力学过程中的原子和非马尔可夫性。结果表明，通过原子-空穴耦合和储层参数可以有效地控制QSLT和非马尔可夫性。原子-空穴耦合和失谐都可能引起从马尔可夫动力学到非马尔可夫动力学的突然跃迁，而这种跃迁是量子加速过程的主要物理原因。从没有加速到加速原子-腔耦合和储层参数的突然转变的临界值。