Revealing non-Markovian Kondo transport with waiting time distributions

We investigate non-Markovian transport dynamics and signatures of the Kondo effect in a single quantum dot (QD) model. The QD is coupled to a left lead non-Markovian bath and weakly coupled to a right lead, acting as a detector. We calculate the waiting time distribution (WTD) of electrons tunneling into the detector using a combination of the hierarchical equations of motion (HEOM) approach and the Born-Markov (BM) approximation. Oscillations emerge in the short-time WTD, becoming more pronounced with stronger left-lead coupling. Fourier analysis reveals a blueshift in the oscillation frequency as coupling increases, indicating enhanced system-bath hybridization. Crucially, comparison with a master equation confirms that these oscillations are a direct consequence of non-Markovian system-bath correlations. By introducing a toy model, we analyze the role of different parameters, such as coupling strength and bandwidth, in significantly influencing the oscillatory behavior in WTD. In addition, we examine the Kondo effect's influence on these oscillations by varying the coupling strength and the bandwidth of the non-Markovian bath. Decreasing the bandwidth and increasing the coupling strength enhance the WTD oscillations, while also enhancing the Kondo resonance in the quantum dot's density of states. Our results demonstrate that WTD oscillations offer a valuable tool for probing non-Markovian system-bath interactions and the emergence of Kondo correlations within QD systems.