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arXiv:0706.2925 · AIP conference proceedings

Non-Markovian dynamics in the theory of full counting statistics

Christian Flindt, Alessandro Braggio, Tomáš Novotný

Published Jan 1, 2007• 7 citations
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Abstract

We consider the theoretical description of real‐time counting of electrons tunneling through a Coulomb‐blockade quantum dot using a detector with finite bandwidth. By tracing out the quantum dot we find that the dynamics of the detector effectively is non‐Markovian. We calculate the cumulant generating function corresponding to the resulting non‐Markovian rate equation and find that the measured current cumulants behave significantly differently compared to those of a Markovian transport process. Our findings provide a novel interpretation of noise suppression found in a number of systems.

DOI
10.1063/1.2759735

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We consider the counting statistics of electron transport through a double quantum dot with special emphasis on the dephasing induced by a nearby charge detector. The double dot is embedded in a dissipative enviroment, and the presence of electrons on the double dot is detected with a nearby quantum point contact. Charge transport through the double dot is governed by a non-Markovian generalized master equation. We describe how the cumulants of the current can be obtained for such problems, and investigate the difference between the dephasing mechanisms induced by the quantum point contact and the coupling to the external heat bath. Finally, we consider various open questions of relevance to future research.
We have investigated the dynamics of bound particles in multilevel current-carrying quantum dots. We look specifically in the regime of resonant tunnelling transport, where several channels are available for transport. Through a non-Markovian formalism under the Born approximation, we investigate the real-time evolution of the confined particles including transport-induced decoherence and relaxation. In the case of a coherent superposition between states with different particle number, we find that a Fock-space coherence may be preserved even in the presence of tunneling into and out of the dot. Real-time results are presented for various asymmetries of tunneling rates into different orbitals.
A detailed understanding of the full measurement statistics in experiments is the basis for thorough device characterization and advanced applications such as quantum metrology. In this spirit, we investigate the conditional counting statistics of an electron-spin-resonance pumped quantum dot (QD), which is tunnel-coupled to a side electrode and continuously monitored by a quantum point contact (QPC). For such a noninvasive detector, we find that the spin current through the QD and its related cumulants exhibit intriguing features and system parameter dependences when conditioned on the QPC current, which are in strong contrast to the unconditional cumulants. By turning the perspective around and considering the counting statistics of the QPC current conditioned on the QD current, we reveal an anomalous conditional QPC current noise, which is surprisingly suppressed for increasing coupling to the environment. Our results show that information backaction can substantially render statistical transport fluctuations. This unique advantage of the conditional counting statistics in probing the underlying correlations between system and detector, even for noninvasive measurements, can thus be employed for improving measurement protocols in quantum metrology.
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We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. The activation rate dependence on the third current cumulant includes an additional term originating from the backaction of the measurement circuit.