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Acta Physica Polonica A

Phonon Effects on the Weak Measurement of Charge States in Quantum Dots with a Quantum Point Contact

Łukasz Marcinowski, Mateusz Krzyżosiak

Published May 1, 2011• 1 citation
Publisher

Abstract

We study theoretically the process of a weak measurement of charge states in a double quantum dot performed by coupling to a quantum point contact.We focus on the interplay of the measurement process with phonon-induced dephasing of delocalized superpositions of electron states and compare the time scales relevant for the dynamics of the open system and for the measurement process: the decoherence rate, the localization rate of the state conditioned on the measurement outcome and the time scale on which information on the system state is gained in the process of the measurement.

DOI
10.12693/aphyspola.119.640

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We study theoretically the process of a weak measurement of charge states in a double quantum dot performed by coupling to a quantum point contact.We focus on the interplay of the measurement process with phonon-induced dephasing of delocalized superpositions of electron states and compare the time scales relevant for the dynamics of the open system and for the measurement process: the decoherence rate, the localization rate of the state conditioned on the measurement outcome and the time scale on which information on the system state is gained in the process of the measurement.
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We study the effect of decoherence on a weak value measurement in a paradigm system consisting of a double quantum dot continuously measured by a quantum point contact. Fluctuations of the parameters controlling the dot state induce decoherence. We find that, for measurements longer than the decoherence time, weak values are always reduced within the range of the eigenvalues of the measured observable. For measurements at shorter time scales, the measured weak value strongly depends on the interplay between the decoherence dynamics of the system and the detector backaction. In particular, depending on the postselected state and the strength of the decoherence, a more frequent classical readout of the detector might lead to an enhancement of weak values.
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Recently, the investigations on the coherent tunnelling in a coupled quantum-dot (QD) system have carried out both experimentally (Blick et al., 1998, and Oosterkamp et al., 1998), and theoretically (Tsukada et al., 1997, and Wu et al., 2000). However, all of these studies did not take the influence of the measurement into account. It is well known that measurement itself will certainly induce dephasing. This effect was studied (Aleiner et at., 1997, Levinson, 1997, and E. Buks et al., 1998) in detail. Also, Gurvitz et al. (1996, 1997) derived modified rate equations and studied the dephasing effect induced by measuring the electron state in a coupled QD system via a quantum point contact.
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.