High-order cumulants in the counting statistics of asymmetric quantum dots

Fricke, Christian; Hohls, Frank; Sethubalasubramanian, Nandhavel; Fricke, Lukas; Haug, Rolf J.

doi:10.1063/1.3430000

Cited by 43 publications

(39 citation statements)

References 20 publications

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“…2a we show numerically exact results for the high-order cumulant n 15 corresponding to the measurements in Ref. 9. Our calculations agree well with the experiment and reproduce the clear oscillations as functions of the dimensionless time τ and the asymmetry a.…”

Section: Low Biassupporting

confidence: 74%

“…At low bias voltages, the quantum dot can only be empty or singly occupied. This corresponds to the recent experiment by Fricke et al, 9 and we show how the measured oscillations of the 15th cumulant as a function of time and coupling to the leads can be explained by the motion of the zeros of the GF. In contrast, the factorial cumulants do not oscillate.…”

Section: 22mentioning

confidence: 99%

“…3,5,6 Although quantum effects are typically suppressed at the long time scales characterizing the charge transport, quantum dots provide a unique setting to experimentally test theoretical predictions for high-order statistics. Remarkably, time-dependent cumulants of the transferred charge beyond the 15th order have recently been measured in single-electron transport through a Coulomb blockade quantum dot [7][8][9] and a wealth of statistical data is now available.…”

Section: Introductionmentioning

confidence: 99%

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Factorial cumulants reveal interactions in counting statistics

2011

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Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures. Recently it has been shown that the charge transport statistics for noninteracting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent singleparticle events, and the zeros of the generating function are real and negative. Here we investigate how the zeros of the generating function move into the complex plane due to interactions and demonstrate that the positions of the zeros can be detected using high-order factorial cumulants. As an illustrative example we consider electron transport through a Coulomb blockade quantum dot for which we show that the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. Our findings are important for understanding the influence of interactions on counting statistics, and the characterization in terms of zeros of the generating function provides us with a simple interpretation of recent experiments, where high-order statistics have been measured.

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Section: Low Biassupporting

confidence: 74%

Section: 22mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Factorial cumulants reveal interactions in counting statistics

2011

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“…3 For example, non-zero higher-order cumulants reflect non-Gaussian behavior. Counting statistics in mesoscopic physics has been a subject of intensive theoretical interest for almost two decades, but recently it has also gained considerable experimental interest: in a series of experiments, [5][6][7][8][9][10][11][12][13][14][15][16][17] high order cumulants and even the entire distribution function of transferred charge have been measured, clearly demonstrating that counting statistics now has become an important concept also in experimental physics.…”

Section: Introductionmentioning

confidence: 99%

Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects

Flindt

Novotný

Braggio³

et al. 2010

Phys. Rev. B

139

200

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Recent experimental progress has made it possible to detect in real-time single electrons tunneling through Coulomb blockade nanostructures, thereby allowing for precise measurements of the statistical distribution of the number of transferred charges, the so-called full counting statistics. These experimental advances call for a solid theoretical platform for equally accurate calculations of distribution functions and their cumulants. Here we develop a general framework for calculating zero-frequency current cumulants of arbitrary orders for transport through nanostructures with strong Coulomb interactions. Our recursive method can treat systems with many states as well as non-Markovian dynamics. We illustrate our approach with three examples of current experimental relevance: bunching transport through a two-level quantum dot, transport through a nano-electromechanical system with dynamical Franck-Condon blockade, and transport through coherently coupled quantum dots embedded in a dissipative environment. We discuss properties of high-order cumulants as well as possible subtleties associated with non-Markovian dynamics.

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“…Direct measurements of the third and higher moments of fluctuations in mesoscopic systems require highly sophisticated techniques. [2][3][4][5] In another approach, following theoretical proposals, [6][7][8][9] non-Gaussian statistics was detected using noise-activated switching out of a metastable state in a Josephson junction. 10,11 This approach provides direct access to the tail of the noise distribution, as a relatively large noise outburst is required to drive the Josephson junction out of the effective potential well.…”

Section: Introductionmentioning

confidence: 99%

Poisson noise induced switching in driven micromechanical resonators

et al. 2012

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We study Poisson-noise induced switching between coexisting vibrational states in driven nonlinear micromechanical resonators. In contrast to Gaussian noise induced switching, the measured logarithm of the switching rate is proportional not to the reciprocal noise intensity, but to its logarithm, for fixed pulse area. We also find that the switching rate logarithm varies as a square root of the distance to the bifurcation point, instead of the conventional scaling with exponent 3/2.

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High-order cumulants in the counting statistics of asymmetric quantum dots

Cited by 43 publications

References 20 publications

Factorial cumulants reveal interactions in counting statistics

Factorial cumulants reveal interactions in counting statistics

Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects

Poisson noise induced switching in driven micromechanical resonators

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