The fluctuation behavior of triple quantum dots (TQDs) has, so far, largely focused on current cumulants in the long-time limit via full counting statistics. Given that TQDs are nontrivial open quantum systems with many interesting features, such as Aharonov-Bohm interference and coherent population blocking, new fluctuating-time statistics, such as the waiting time distribution (WTD), may provide more information than just the current cumulants alone. In this paper, we use a Born-Markov master equation to calculate the standard and higher-order WTDs for coherently coupled TQDs arrayed in triangular ring geometries for several transport regimes. In all cases, we find that the WTD displays coherent oscillations that correspond directly to individual time-dependent dot occupation probabilities, a result also reported recently [G. Engelhardt and J. Cao, Phys. Rev. B 99, 075436 (2019)]. Our analysis, however, goes beyond the single-occupancy and single waiting time regimes, investigating waiting time behavior for TQDs occupied by multiple electrons and with finite electron-electron interactions. We demonstrate that in these regimes of higher occupancy, quantum coherent effects introduce correlations between successive waiting times, which we can tune via an applied magnetic field. We also show that correlations can be used to distinguish between TQD configurations that have identical full counting statistics and that dark states can be tuned with Aharonov-Bohm interference for more complicated regimes than single occupancy.

中文翻译：

---

三角形三重量子点中的相干时间相关振荡和时间相关性

到目前为止，三重量子点 (TQD) 的波动行为主要通过完整的计数统计集中在长时间限制内的当前累积量上。鉴于 TQD 是具有许多有趣特征的非平凡开放量子系统，例如 Aharonov-Bohm 干扰和相干种群阻塞，新的波动时间统计数据，例如等待时间分布 (WTD)，可能会提供比仅当前累积量更多的信息. 在本文中，我们使用 Born-Markov 主方程来计算以三角环几何结构排列的相干耦合 TQD 的标准和高阶 WTD，用于几种传输机制。在所有情况下，我们发现 WTD 显示出相干振荡，直接对应于个体时间相关的点占据概率，最近也报道了一个结果 [G. 恩格尔哈特和 J.物理。修订版 B 99 , 075436 (2019)]。然而，我们的分析超越了单占用和单等待时间制度，研究了由多个电子占据且具有有限电子-电子相互作用的 TQD 的等待时间行为。我们证明，在这些较高占用率的情况下，量子相干效应会在连续等待时间之间引入相关性，我们可以通过施加的磁场对其进行调整。我们还表明，相关性可用于区分具有相同完整计数统计数据的 TQD 配置，并且可以使用 Aharonov-Bohm 干扰对暗状态进行调整，以用于比单一占用更复杂的状态。