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arXiv:0809.1837 · Journal of Statistical Mechanics Theory and Experiment

The influence of charge detection on counting statistics

Alessandro Braggio, Christian Flindt, Tomáš Novotný

Published Jan 8, 2009• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1742-5468/2009/01/p01048

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Quantum measurement always disturbs the quantum system being measured, which is known as measurement-induced backaction. We consider a specific model, a double quantum dot charge qubit measured by a nearby quantum point contact. We explore the evolution by deriving a master equation. The advantages of this master equation are (i) it has the Lindblad form and the non-Markovian effects are embodied in the time-dependent coefficients, (ii) the tunnelling and decay effect can be clearly understood in the master equation, and (iii) it can be further easily controlled by manipulate the Hamiltonian.
We investigate a tunnel contact coupled to a double quantum dot (DQD) and employed as a charge monitor for the latter. We consider both the classical limit and the quantum regime. In the classical case, we derive measurement correlations from conditional probabilities, yielding quantitative statements about the parameter regime in which the detection scheme works well. Moreover, we demonstrate that not only the DQD occupation but also the corresponding current may strongly correlate with the detector current. The quantum-mechanical solution, obtained with a Bloch-Redfield master equation, shows that the backaction of the measurement tends to localize the DQD electrons, and thus significantly reduces the DQD current. Moreover, it provides the effective parameters of the classical treatment. It turns out that already the classical description is adequate for most operating regimes.
In this paper, we develop a nonperturbation theory for describing decoherence dynamics of electron charges in a double quantum dot gated by electrodes. We extend the Feynman-Vernon influence functional theory to fermionic environments and derive an exact master equation for the reduced density matrix of electrons in the double dot for a general spectral density at arbitrary temperature and bias. We then investigate the decoherence dynamics of the double-dot charge qubit with backreaction of the reservoirs being fully taken into account. Time-dependent fluctuations and leakage effects induced from the dot-reservoir coupling are explicitly explored. The charge qubit dynamics from the Markovian to non-Markovian regime is systematically studied under various manipulating conditions. The decay behavior of charge qubit coherence and the corresponding relaxation time T1{T}_{1}T1​ and dephasing time T2{T}_{2}T2​ are analyzed in detail.
We study the dynamics of a double quantum dot (DQD) system interacting with a Gaussian white noise (GWN) environment which is measured by a quantum point contact (QPC) device. With both the transverse and longitudinal noise taken into account, we utilize an effective method by adding an additional Bloch vector to calculate the cumulant generating functions of the electron transfer in the QPC detector based on the full counting statistics. We study the average detector current, Fano factor, and average waiting time of the electron transfer in the presence of decoherence effects of the DQD system caused by both the QPC and the GWN environment. It indicates that the decoherence effects arising from the QPC and the GWN environment have obviously different influences on the electron transfer detected by the QPC device in both short-time and long-time limits. It is shown that the measurement process would localize the electron in a DQD in a short time and that the distribution of the average current and Fano factor versus level displacement in long-time limit are broadened due to the interaction between the system and GWN environment, which provides a reliable method to explore the dynamical behavior of an open quantum system and to extract the characteristics of the environment by analyzing the detector outcome. Our results provide theoretical support for studies of quantum measurement in a semiconductor device affected by a fluctuant environment.