  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 non-trivial 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 coherentlycoupled 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 in Ref.[1]. 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 FCS and that dark
states can be tuned with Aharonov-Bohm interference for more complicated
regimes than single-occupancy.
