Electron Waiting Times in a Strongly Interacting Quantum Dot: Interaction Effects and Higher-Order Tunneling Processes

Abstract

Distributions of electron waiting times have been measured in several recent experiments and have been shown to provide complementary information compared with what can be learned from the electric current fluctuations. Existing theories, however, are restricted to either weakly coupled nanostructures or phasecoherent transport in mesoscopic conductors. Here, we consider an interacting quantum dot and develop a real-time diagrammatic theory of waiting time distributions that can treat the interesting regime, in which both interaction effects and higher-order tunneling processes are important. Specifically, we find that our quantum-mechanical theory captures higher-order tunneling processes at low temperatures, which are not included in a classical description, and which dramatically affect the waiting times by allowing fast tunneling processes inside the Coulomb blockade region. Our work paves the way for systematic investigations of temporal fluctuations in interacting quantum systems, for example close to a Kondo resonance or in a Luttinger liquid.

Higher-Order Photon Statistics as a New Tool to Reveal Hidden Excited States in a Plasmonic Cavity

“…A quantity providing complementary information to the correlation functions is the waiting-time distribution w(t) [36][37][38][39][40][41][42][43][44][45][46][47][48]. It is the probability density that two consecutive photons are detected at the time difference t. The distribution can be expressed as w(t) = τ ∂ 2 t P 0 (t), where τ is the mean waiting time and P 0 is the idle-time probability that no photons have been counted during the time span [0, t] [74].…”

“…Nevertheless, the difference between both quantities is small for times smaller than the average waiting time. Waiting times have been used frequently to study the statistics of electron currents in nanoscale junctions [38][39][40][41][42][43][44][45][46][47][48][49][50] and enzymatic reactions [32,[51][52][53][54][55][56]. However, they have been used seldom in the analysis of single-photon emitters [36,37].…”

Electronic statistics-on-demand: bunching, anti-bunching, positive and negative correlations in a molecular spin-valve

“…While a relatively recent addition to the analysis of charge fluctuations in open quantum systems [27], waiting time theory has developed rapidly in the last 10 years. Consequently, it has been used to investigate a wide variety of transport scenarios, such as tunneling through molecules with electron-electron [27][28][29][30] and electronphonon [31][32][33][34] interactions, telegraphic switching [35], double [36,37] and triple [38,39] quantum dots, superconducting junctions [40][41][42][43][44], coherent conductors [45][46][47], non-Markovian transport [48,49], periodically driven transport [50,51], and transport in the transient regime [52][53][54][55]. As opposed to the full counting statistics (FCS), which is the most prevalent method for analyzing charge fluctuations, the WTD provides information on transport at short timescales, particularly via correlations between successive waiting times [28,50,51,[56][57][58].…”

“…The spin quantization axis of the source electrode is aligned with the z-axis, whereas the drain electrode is allowed to rotate along the x − z plane, enclosing an angle φ with the z−axis. and time-dependent FCS have also been previously used to analyze the coherent dynamics present in this system, finding that Larmor precession causes coherent oscillations in the WTD and time-dependent charge cumulants [6,48]. Tang et al have also recently developed the theory of spin-resolved waiting times in a quantum dot spin-valve [10].…”

Higher-Order Photon Statistics as a New Tool to Reveal Hidden Excited States in a Plasmonic Cavity

“…The waiting-time distribution w between successive photon emission events can be constructed from all orders of the correlation functions g ( m ) , but is also directly measurable in experiment. − The distribution characterizes photon bunching and antibunching in a more precise manner than the second-order correlation function. ,, Nevertheless, the difference between both quantities is small for times smaller than the average waiting time. Waiting times have been used frequently to study the statistics of electron currents in nanoscale junctions − and enzymatic reactions. ,− However, they have been used seldom in the analysis of single-photon emitters. , …”