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Journal of Semiconductors

Quantum Measurement of Single Electron State by a Mesoscopic Detector

Xue-Ning Hu, JunYan Luo, Xin-Qi Li

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

A realistic measurement setup for a system such system measured by a mesoscopie detector,is theoretically as a charged two-state （qubit） or multi-state quantum studied. To properly describe the measurement-induced back-action,a detailed-balance preserved quantum master equation treatment is developed. The established framework is applicable for arbitrary voltages and temperatures.

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Full text: Recently, we presented a model for continuous DC-biased measurement of a coupled quantum dot (CQD) charge qubit by realistic measurement devices. Modelling realistic measurement devices as ideal detectors embedded in an equivalent measurement circuit (see figure), our aim was to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit, i.e. the measured current. We generalised a recently developed quantum trajectory theory for realistic photodetectors to treat solid-state detectors-primarily a single electron transistor (SET). This method yields stochastic equations whose (numerical) solutions are the 'realistic quantum trajectories' of the conditioned qubit state. Here we present numerical solutions and analysis for the SET equations. The solutions elucidate the regimes in which (Rabi) electron tunnelling between the CQDs can be detected in a realistic measurement. Further to this, the solutions reveal the conditions under which electron tunnelling events through the SET can be observed, which is related to the question of the nature of the back-action noise of the SET. Copyright (2005) Australian Institute of Physics.

•Jul 1, 2005•0 citations

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•Jan 1, 2006•0 citations
A realistic measurement setup for a system such system measured by a mesoscopie detector,is theoretically as a charged two-state （qubit） or multi-state quantum studied. To properly describe the measurement-induced back-action,a detailed-balance preserved quantum master equation treatment is developed. The established framework is applicable for arbitrary voltages and temperatures.
Quantum measurement of a solid-state qubit by a mesoscopic detector is of fundamental interest in quantum physics and an essential issue in quantum computing. In this work, by employing a unified quantum master equation approach constructed in our recent publications, we study the measurement-induced relaxation and dephasing of the coupled-quantum-dot states measured by a quantum-point contact. Our treatment pays particular attention on the detailed-balance relation, which is a consequence of properly accounting for the energy exchange between the qubit and detector during the measurement process. As a result, our theory is applicable to measurement at arbitrary voltage and temperature. Both numerical and analytical results for the qubit relaxation and dephasing are carried out, and important features are highlighted in concern with their possible relevance to future experiments.
Closely related to the quantum information processing in solid states, we study the quantum measurement of single electron state by a mesoscopic charge-sensitive detector, namely the quantum point contact (QPC). We find that the conventional Lindblad-type master equation is not appropriate for describing the underlying measurement dynamics. The treatment developed in this work properly accounts for the energy-exchange between the detector and the measured system, and its role on the detailed-balance relation. A valid description for the QPC measurement dynamics is provided which may have impact on the study of quantum measurement and quantum feedback control in solid states.
Quantum point contact (QPC), one of the typical mesoscopic transport devices, has been suggested to be an efficient detector for quantum measurement. In the context of two-state charge qubit, our previous studies showed that the QPC's measurement back-action cannot be described by the conventional Lindblad quantum master equation. In this work, we study the measurement problem of a multistate system, say, an electron in disordered potential, subject to the quantum measurement of the mesoscopic detector QPC. The effect of measurement back-action and the detector's readout current are analyzed, where particular attention is focused on some new features and the underlying physics associated with the measurement-induced delocalization versus the measurement voltages.
Full text: Recently, we presented a model for continuous DC-biased measurement of a coupled quantum dot (CQD) charge qubit by realistic measurement devices. Modelling realistic measurement devices as ideal detectors embedded in an equivalent measurement circuit (see figure), our aim was to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit, i.e. the measured current. We generalised a recently developed quantum trajectory theory for realistic photodetectors to treat solid-state detectors-primarily a single electron transistor (SET). This method yields stochastic equations whose (numerical) solutions are the 'realistic quantum trajectories' of the conditioned qubit state. Here we present numerical solutions and analysis for the SET equations. The solutions elucidate the regimes in which (Rabi) electron tunnelling between the CQDs can be detected in a realistic measurement. Further to this, the solutions reveal the conditions under which electron tunnelling events through the SET can be observed, which is related to the question of the nature of the back-action noise of the SET. Copyright (2005) Australian Institute of Physics.