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physica status solidi (b)

Optimal single‐electron feedback control

Timo Wagner, Johannes C. Bayer, Eddy P. Rugeramigabo, R. J. Haug

Published Jan 4, 2017• 3 citations
Publisher

Abstract

Abstract In a closed‐loop controlled single‐electron transistor (SET) the optimal feedback response is investigated, leading to a maximum suppression of shot‐noise. Using a coupled quantum point contact (QPC) charge detector, the tunneling process is monitored in real‐time and the fluctuations are fed back periodically to the tunneling barriers of the SET. The feedback response is applied proportional to the deviation from the target number of average transferred electrons. This leads to a strong suppression and temporal saturation of the cumulants of the full counting statistics. For the optimal feedback response, the saturation value of second cumulant is found to be given by target number. Astonishingly, the feedback works robust even for target numbers much smaller than one.

DOI
10.1002/pssb.201600701

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Abstract In a closed‐loop controlled single‐electron transistor (SET) the optimal feedback response is investigated, leading to a maximum suppression of shot‐noise. Using a coupled quantum point contact (QPC) charge detector, the tunneling process is monitored in real‐time and the fluctuations are fed back periodically to the tunneling barriers of the SET. The feedback response is applied proportional to the deviation from the target number of average transferred electrons. This leads to a strong suppression and temporal saturation of the cumulants of the full counting statistics. For the optimal feedback response, the saturation value of second cumulant is found to be given by target number. Astonishingly, the feedback works robust even for target numbers much smaller than one.
We consider charge qubit monitoring (continuous-in-time weak measurement) by a single-electron transistor (SET) operating in the sequential-tunneling regime. We show that commonly used master equations for this regime are not of the Lindblad form that is necessary and sufficient for guaranteeing valid physical states. In this paper we derive a Lindblad-form master equation and a corresponding quantum trajectory model for continuous measurement of the charge qubit by a SET. Our approach requires that the SET-qubit coupling be strong compared to the SET tunneling rates. We present an analysis of the quality of the qubit measurement in this model (sensitivity versus back action). Typically, the strong coupling when the SET island is occupied causes back action on the qubit beyond the quantum back action necessary for its sensitivity, and hence the conditioned qubit state is mixed. However, in one strongly coupled, asymmetric regime, the SET can approach the limit of an ideal detector with an almost pure conditioned state. We also quantify the quality of the SET using more traditional concepts such as the measurement time and decoherence time, which we have generalized so as to treat the strongly responding regime.
A controllable low noise current lies at the heart of high-precision measurements in quantum transport and metrology. While the previous research dealt with the suppression of noise in transport through a tunneling junction or a single quantum dot (QD) device, the present work investigates noise inhibition of a double quantum dot (DQD) transport system based on closed-loop feedback control. The unique advantage of a DQD device is that bidirectional transport at low bias can be measured by a nearby quantum point contact. However, the continuous monitoring of the DQD states inevitably leads to a measurement-induced dephasing. To appropriately characterize its transport properties in the presence of feedback action, we here develop a numerical method dubbed auxiliary density matrix approach, motivated by the hierarchical expansion of the moment-generating function in the hierarchy equations of motion [J. Cerrillo et al., Phys. Rev. B 94, 214308 (2016)]. This generic method has no restriction on the system structure and parameters and is able to evaluate the feedback current cumulants to an arbitrary order. It is revealed that the feedback control of the tunnel coupling between the two dots is the most effective to suppress the noise under various tunnel coupling configurations. The influence of interdot Coulomb interaction, measurement-induced dephasing, and finite time delay on feedback is also analyzed in detail.
The current through nanostructures like quantum dots can be stabilized by a classical feedback loop that continuously adjusts system parameters as a function of the number of tunnelled particles n. At large times, the feedback loop freezes the fluctuations of n, which leads to highly accurate, continuous single particle transfers. For the simplest case of feedback acting simultaneously on all system parameters, we show how to reconstruct the original full counting statistics from the frozen distribution.
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.
We propose the manipulation of an isolated qubit by a simple instantaneous closed-loop feedback scheme in which a time-dependent electronic detector current is directly back-coupled into qubit parameters. As a specific detector model, we employ a capacitively coupled single-electron transistor. We demonstrate the stabilization of pure delocalized qubit states above a critical detector-qubit coupling. This electronic purification is independent of the initial qubit state and is accomplished after few electron jumps through the detector. Our simple scheme can be used for the efficient and robust initialization of solid-state qubits in quantum computational algorithms at arbitrary temperatures.