We study the non-Markovianity and quantum speedup of a two-level atom (quantum system of interest) in a dissipative Jaynes-Cumming model, where the atom is embedded in a single-mode cavity, which is leaky being coupled to an external reservoir with Ohmic spectral density. We obtain the non-Markovianity characterized by using the probability of the atomic excited state and the negative decoherence rate in the time-local master equation. We also calculate the quantum speed limit time (QSLT) of the evolution process of the atom. The results show that, the atom-cavity coupling is the main physical reasons of the transition from Markovian to non-Markovian dynamics and the transition from no speedup to speedup process, and the critical value of this sudden transition only depends on the Ohmicity parameter. The atom-cavity coupling and the appropriate reservoir parameters can effectively improve the non-Markovianity in the dynamics process and speed up the evolution of the atom. Moreover, the initial non-Markovian dynamics first turns into Markovian and then back to non-Markovian with increasing the atom-cavity coupling under certain condition. Finally, the physical interpretation is provided.

中文翻译：

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基于欧姆储层的非马尔可夫性和量子限速时间

我们研究了耗散 Jaynes-Cumming 模型中两级原子（感兴趣的量子系统）的非马尔可夫性和量子加速，其中原子嵌入单模腔中，该腔泄漏耦合到外部储层具有欧姆谱密度。我们通过使用时域主方程中原子激发态的概率和负退相干率来获得非马尔可夫性。我们还计算了原子演化过程的量子限速时间（QSLT）。结果表明，原子-腔耦合是马尔可夫动力学向非马尔可夫动力学转变以及从无加速向加速过程转变的主要物理原因，而这种突然转变的临界值仅取决于Ohmicity参数。原子-腔耦合和合适的储层参数可以有效改善动力学过程中的非马尔可夫性，加速原子的演化。而且，初始的非马尔可夫动力学在一定条件下随着原子-腔耦合的增加首先转变为马尔可夫，然后又回到非马尔可夫。最后，提供物理解释。