Coherent time-dependent oscillations and temporal correlations in triangular triple quantum dots

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 fluctuatingtime 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.