Factorial cumulants reveal interactions in counting statistics

Kambly, Dania; Flindt, Christian; Büttiker, Μ.

doi:10.1103/physrevb.83.075432

Cited by 82 publications

(110 citation statements)

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“…(1) to attain complex values, [30][31][32][33] similarly to the Yang-Lee theory of phase transitions. 34 This idea is based on the recent observation that, upon transforming λ into u,…”

Section: Introductionmentioning

confidence: 92%

Full-counting statistics for molecular junctions: Fluctuation theorem and singularities

et al. 2013

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We study the full-counting statistics of charges transmitted through a single-level quantum dot weakly coupled to a local Einstein phonon which causes fluctuations in the dot energy. An analytic expression for the cumulant generating-function, accurate up to second order in the electron-phonon coupling and valid for finite voltages and temperatures, is obtained in the extended wide-band limit. The result accounts for nonequilibrium phonon distributions induced by the source-drain bias voltage, and concomitantly satisfies the fluctuation theorem. Extending the counting field to the complex plane, we investigate the locations of possible singularities of the cumulant generatingfunction, and exploit them to identify regimes in which the electron transfer is affected differently by the coupling to the phonons. Within a large-deviation analysis, we find a kink in the probability distribution, analogous to a first-order phase transition in thermodynamics, which would be a unique hallmark of the electron-phonon correlations. This kink reflects the fact that although inelastic scattering by the phonons once the voltage exceeds their frequency can scatter electrons opposite to the bias, this will never generate current flowing against the bias at zero temperature, in accordance with the fluctuation theorem.

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“…(1) to attain complex values, [30][31][32][33] similarly to the Yang-Lee theory of phase transitions. 34 This idea is based on the recent observation that, upon transforming λ into u,…”

Section: Introductionmentioning

confidence: 92%

Full-counting statistics for molecular junctions: Fluctuation theorem and singularities

et al. 2013

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“…No zero-crossing oscillations in FCs are observed consistent with a two-level Markovian model. 34 The white arrows point to the development of faint non-zero-crossing oscillations appearing in higher order FCs probably due to finite statistics.…”

Section: Appendixmentioning

confidence: 99%

“…Due to the logarithmic scaling of the FCs the latter plot is more convenient to follow the evolution of the results. 34 Note that consecutive FCs alternate sign as indicated by red and blue colors. For a two-state Markovian system no oscillations in the factorial cumulants are expected in agreement with the fact that there is no clear zero-crossing oscillations in the data.…”

Section: F Normal Vs Factorial Cumulantsmentioning

confidence: 99%

“…16 However, it is difficult to extract any useful information directly from normal cumulants as the poles of the cumulant generating function are displaced from the real axis by construction. Recently, Kambly et al 34 proposed the use of factorial cumulants (FCs) for this purpose as any zerocrossing oscillations in the latter directly indicate the offset of ZGF from the real axis pointing towards relevance of interactions. We have calculated the first twelve FCs from our data which are shown in Fig.…”

Section: F Normal Vs Factorial Cumulantsmentioning

confidence: 99%

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Counting statistics of hole transfer in ap-type GaAs quantum dot with dense excitation spectrum

et al. 2013

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Low-temperature transport experiments on a p-type GaAs quantum dot capacitively coupled to a quantum point contact are presented. The time-averaged as well as time-resolved detection of charging events of the dot are demonstrated and they are used to extract the tunnelling rates into and out of the quantum dot. The extracted rates exhibit a super-linear enhancement with the bias applied across the dot which is interpreted in terms of a dense spectrum of excited states contributing to the transport, characteristic for heavy hole systems. The full counting statistics of charge transfer events and the effect of back action is studied. The normal cumulants as well as the recently proposed factorial cumulants are calculated and discussed in view of their importance for interacting systems.

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“…1 but measuring instead the fluctuations of a conserved U(1) charge such as particle numberN and spin S z reveals important features of quantum many-body systems including their entanglement properties, quite similarly to the way in which Full Counting Statistics (FCS), the study of charge transfer across mesoscopic conductors, has been intensely analyzed in mesoscopic transport [50][51][52][53][54] and in cold atom systems [55,56]. Indeed, our result for non-interacting fermions unequivocally demonstrates the importance of studying the full set of cumulants, beyond the fluctuations (noise) encoded in the second cumulant.…”

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confidence: 99%

Bipartite fluctuations as a probe of many-body entanglement

et al. 2012

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We investigate in detail the behavior of the bipartite fluctuations of particle numberN and spin S z in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

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Factorial cumulants reveal interactions in counting statistics

Cited by 82 publications

References 50 publications

Full-counting statistics for molecular junctions: Fluctuation theorem and singularities

Full-counting statistics for molecular junctions: Fluctuation theorem and singularities

Counting statistics of hole transfer in ap-type GaAs quantum dot with dense excitation spectrum

Bipartite fluctuations as a probe of many-body entanglement

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