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Continuous Weak Measurement of Qubit Oscillations with Strongly Responding Single Electron Transistors

HuJun Jiao, Shi-Kuan Wang, Feng Li, Xin-Qi Li

Published Jun 16, 2008• 0 citations
OpenAlex

Abstract

We investigate the continuous weak measurement of a solid-state qubit by single electron transistors in nonlinear response regime. It is found that the signal-to-noise ratio can violate the universal upper bound imposed quantum mechanically to any linear response detectors. We understand the violation by means of the cross-correlation of the detector currents.

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We investigate the continuous weak measurement of a solid-state qubit by single electron transistors in nonlinear response regime. It is found that the signal-to-noise ratio can violate the universal upper bound imposed quantum mechanically to any linear response detectors. We understand the violation by means of the cross-correlation of the detector currents.
In this paper we consider the continuous weak measurement of a solid‐state qubit by single electron transistors (SET). For single‐dot SET, we find that in nonlinear response regime the signal‐to‐noise ratio can violate the universal upper bound imposed quantum mechanically on any linear response detectors. We understand the violation by means of the cross‐correlation of the detector currents. For double‐dot SET, we discuss its robustness against wider range of temperatures, quantum efficiency, and the relevant open issues unresolved.
Qubit measurement by mesoscopic charge detectors has received great interest in the community of mesoscopic transport and solid-state quantum computation, and some controversial issues still remain unresolved. In this work, we revisit the continuous weak measurement of a solid-state qubit by single electron transistors (SETs) in nonlinear-response regime. For two SET models typically used in the literature, we find that the signal-to-noise ratio can violate the universal upper bound ``4,'' which is imposed quantum mechanically on linear-response detectors. This different result can be understood by means of the cross correlation of the detector currents by viewing the two junctions of the single SET as two detectors. Possible limitation of the potential-scattering approach to this result is also discussed.
We investigate the advantages of using two independent, linear detectors for continuous quantum measurement. For single-shot measurement, the detection process may be quantum limited if the detectors are twins. For weak continuous measurement, cross correlations allow a violation of the Korotkov-Averin bound for the detector's signal-to-noise ratio. The joint weak measurement of noncommuting observables is also investigated, and we find the cross correlation changes sign as a function of frequency, reflecting a crossover from incoherent relaxation to coherent, out of phase oscillations. Our results are applied to a double quantum-dot charge qubit, simultaneously measured by two quantum point contacts.
We consider the problem of continuous quantum measurement of coherent oscillations between two quantum states of an individual two-state system. It is shown that the interplay between the information acquisition and the backaction dephasing of the oscillations by the detector imposes a fundamental limit, equal to four, on the signal-to-noise ratio of the measurement. The limit is universal, e.g., independent of the coupling strength between the detector and system, and results from the tendency of quantum measurement to localize the system in one of the measured eigenstates.
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.