Waiting time distribution revealing the internal spin dynamics in a double quantum dot

Abstract

Waiting time distribution and the zero-frequency full counting statistics of unidirectional electron transport through a double quantum dot molecule attached to spin-polarized leads are analyzed using the quantum master equation. The waiting time distribution exhibits a non-trivial dependence on the value of the exchange coupling between the dots and the gradient of the applied magnetic field, which reveals the oscillations between the spin states of the molecule. The zero-frequency full counting statistics, on the other hand, is independent of the aforementioned quantities, thus giving no insight into the internal dynamics. The fact that the waiting time distribution and the zero-frequency full counting statistics give a non-equivalent information is associated with two factors. Firstly, it can be explained by the sensitivity to different timescales of the dynamics of the system. Secondly, it is associated with the presence of the correlation between subsequent waiting times, which makes the renewal theory, relating the full counting statistics and the waiting time distribution, not longer applicable. The study highlights the particular usefulness of the waiting time distribution for the analysis of the internal dynamics of mesoscopic systems.

Counting quantum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport

“…Since the variance and mean of a Poisson process are equal, the Fano factor can be used to characterise current distributions as either sub-Poissonian (F < 1), Poissonian (F = 1), or super-Poissonian (F > 1), and consequently identify the transport effects causing this behavior. Indeed, super-Poissonian noise is caused by a host of physical effects, such as the dynamical channel blockade [79,101], asymmetric couplings [19], avalanching electrons [50], telegraphic switching [13,15,40,41], and negative differential resistance [17].…”

“…Unlike FCS, which in quantum master equations is generally restricted to the long time regime, waiting times have no such restriction and can thus provide insight into interesting physics on short timescales. Phenomena such as inelastic interactions [28,38], quantum coherence [35,111], fermionic statistics [37,40], spin-polarised leads [41], and superconducting junctions [108,109] have all been shown to produce temporal correlations observable from the WTD. Experimentally, however, waiting times do have several drawbacks.…”

“…Alternatively, one could repeatedly measure the time τ it takes for the number of measured quantum jumps to reach n and construct a probability density distribution P (τ (n)), as we demonstrate in Fig.(1). The first quantity, n(t), is an example of a fixed-time statistic [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], while τ (n) is an example of a fluctuating-time statistic [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Considering the important role time-dependent fluctuations have, analysis of quantum fluctuations has therefore been focused on calculating either fixed-time and fluctuating-time statistics, and exploring the relationship between the two [42][43][44][45].…”

Numerically exact full counting statistics of the energy current in the Kondo regime

“…These higher order statistical cumulants, and their underlying probability distributions, are obtained from the cumulant generating function for the FCS, and can reveal a whole range of information not present in the first moment. 53 This includes particle traversal times, 54 waiting time distributions [55][56][57][58][59] shot noise 13,15,60 and associated quasiparticle charges. 61 In addition, the steady state cumulant generating function can be related to fluctuations in the thermal efficiency.…”

Nonrenewal statistics in quantum transport from the perspective of first-passage and waiting time distributions

“…3,[8][9][10] The second current cumulant, the zero-frequency noise, can reveal the internal dynamics of the molecule [11][12][13] . For example, super-Poissonian shot noise has many origins: it can arise from telegraphic switching due to spin-polarised leads 14,15 or inelastic cotunneling 16,17 ; negative differential resistance due to asymmetric coupling 18 ; the dynamical channel blockade 19 ; or avalanching electrons due to interactions with a vibrational mode 20 . Higher order cumulants are necessary to fully characterise the transport when the current distribution is non-Gaussian [21][22][23] .…”