Distribution of residence times as a marker to distinguish different pathways for quantum transport

Abstract

Electron transport through a nanoscale system is an inherently stochastic quantum mechanical process. Electric current is a time series of electron tunnelling events separated by random intervals. Thermal and quantum noise are two sources of this randomness. In this paper, we used the quantum master equation to consider the following questions: (i) Given that an electron has tunnelled into the electronically unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there were no intermediate tunnelling events ("the" tunnelling path)? (ii) Given that an electron has tunnelled into the unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there were no intermediate tunnelling events ("an" tunnelling path)? (iii) What are the distributions of these times? We show that electron correlations suppress the difference between the and an electron tunnelling paths.Recently, there have been significant advances towards theoretical and experimental understanding of quantum electron transport through nanoscale systems. In the past, nanoelectronics research was largely focussed on the study of current-voltage characteristics, the main (macroscopic) observable from which information about microscopic details of electron transport is deduced. However, in recent years, the interest in current fluctuations has grown enormously due to the important physical information contained within them [1]. Additionally, current fluctuations started to play important role in single-molecule electronics determining intricate details of interface chemistry and electron-vibrational coupling [2][3][4][5][6][7][8][9][10] The waiting time distribution (WTD) is a natural physical quantity that describes the quantum transport of single electrons. WTDs for successive physical events have been extensively studied as tools to describe stochastic processes in a diverse range of fields, from applied mathematics and astrophysics to single-molecule chemistry [11][12][13][14][15]. WTDs were first applied to quantum processes in the 1980s in photon counting quantum optics experiments [16][17][18]. Recently, WTDs have been used to describe the statistics of single electron transport in nanoscale quantum systems. In 2008 Brandes published his seminal paper on WTDs in quantum transport [19]. His methodology succinctly calculates the distribution of waiting times for various pairs of electron tunnelling events in open quantum systems described by general Markovian master equations. Furthermore, the formalism highlights the connections between WTDs and other important statistical tools for describing stochastic quantum processes, such as shot noise, current fluctuations, and full counting statistics. Recently, Goswami and Harbola used Brandes' approach and the Lindblad master equation to study stochas...

Waiting time distributions in a two-level fluctuator coupled to a superconducting charge detector

“…Electron waiting times have been investigated for a wide range of physical systems including quantum dots, [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] coherent conductors, 36,37 molecular junctions, 38,39 and superconducting systems. [40][41][42][43][44][45][46] Distributions of waiting times contain complementary information on charge transport properties which is not necessarily encoded in the full counting statistics (FCS) and vice versa.…”

Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction

“…[2][3][4][5][6][7][8][9][10][11] The statistical properties of the waiting times are usually studied using waiting time distribution (WTD), which is a conditional probability distribution that we observe the electron transfer in the detector electrode (drain or source) at time t + τ given that an electron was detected in the same electrode at time t.…”

“…[2][3][4][6][7][8][9][10][11]13,14 The question which we discuss in this paper is the following. When an electron transfers through a molecular junction, is there exists a correlation between waiting times for successive electron tunneling or they are statistically independent?…”

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

“…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].…”