Short-time counting statistics of charge transfer in Coulomb-blockade systems

Stegmann, Philipp; König, Jürgen

doi:10.1103/physrevb.94.125433

Cited by 37 publications

(29 citation statements)

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“…For example, it may be useful also for obtaining the transients of the counting statistics of time-independent conductors such as those studied in Refs. [31,45,46]. Moreover, it may be applied to non-Markovian effects that can be captured by time-local master equations with time-dependent coefficients [47].…”

Section: Discussionmentioning

confidence: 99%

Full-counting statistics of time-dependent conductors

2016

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We develop a scheme for the computation of the full-counting statistics of transport described by Markovian master equations with an arbitrary time dependence. It is based on a hierarchy of generalized density operators, where the trace of each operator yields one cumulant. This direct relation offers a better numerical efficiency than the equivalent number-resolved master equation. The proposed method is particularly useful for conductors with an elaborate time dependence stemming, e.g., from pulses or combinations of slow and fast parameter switching. As a test bench for the evaluation of the numerical stability, we consider time-independent problems for which the full-counting statistics can be computed by other means. As applications, we study cumulants of higher order for two time-dependent transport problems of recent interest, namely steady-state coherent transfer by adiabatic passage (CTAP) and Landau-Zener-Stückelberg-Majorana (LZSM) interference in an open double quantum dot.

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Section: Discussionmentioning

confidence: 99%

Full-counting statistics of time-dependent conductors

2016

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“…The corresponding factorial cumulants

C_{normalF, m} false(t false) : = 〈 〈 N^{false(m false)} 〉 〉 false(t false)

are obtained from

C_{normalF, m} false(t false) : = \frac{\partial^{m}}{\partial z^{m}} ln M_{F} false(z, t false) {-2 |}_{z = 0} .

In the context of single‐electron tunneling, the use of factorial rather than ordinary cumulants has been suggested as a convenient tool to identify interactions in the system. Furthermore, factorial and generalized factorial cumulants () have been analyzed in the short‐time limit to detect the presence of fundamental tunneling processes (such as Andreev tunneling) of two electrons simultaneously (). Here, we are going to use factorial cumulants to probe the violation of detailed balance by comparing

C_{normalF, m}^{in} false(t false)

with

C_{normalF, m}^{out} false(t false)

.…”

Section: Stochastic Systemsmentioning

confidence: 99%

Violation of detailed balance for charge‐transfer statistics in Coulomb‐blockade systems

Stegmann

König

2016

Physica Status Solidi (b)

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We discuss the possibility to generate in Coulomb‐blockade systems steady states that violate detailed balance. This includes both voltage biased and non‐biased scenarios. The violation of detailed balance yields that the charge‐transfer statistics for electrons tunneling into an island experiencing strong Coulomb interaction is different from the statistics for tunneling out. This can be experimentally tested by time‐resolved measurement of the island's charge state. We demonstrate this claim for two model systems.

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“…Those artificial two-electron processes (pair-tunneling events) result in completely different statistics for short times t=τ det . Instead of equation (19), we observe in the short-time limit for all even cumulants C t [49]. As a consequence, despite a small variance in the experimental data, the cumulants should not be trusted below t<τ det .…”

Section: Finite-resolution Detectormentioning

confidence: 61%

Revealing attractive electron–electron interaction in a quantum dot by full counting statistics

2018

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Recent experiments (2015 Nature 521 196; 2017 Nat. Commun. 8 395) have presented evidence for electron pairing in a quantum dot beyond the superconducting regime. Here, we show that the impact of an attractive electron-electron interaction on the full counting statistics of electron transfer through a quantum dot is qualitatively different from the case of a repulsive interaction. In particular, the sign of higher-order (generalized) factorial cumulants reveals more pronounced correlations, which even survive in the limit of fast spin relaxation.

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Short-time counting statistics of charge transfer in Coulomb-blockade systems

Cited by 37 publications

References 50 publications

Full-counting statistics of time-dependent conductors

Full-counting statistics of time-dependent conductors

Violation of detailed balance for charge‐transfer statistics in Coulomb‐blockade systems

Revealing attractive electron–electron interaction in a quantum dot by full counting statistics

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