Sensitivity and back-action in charge qubit measurements by a strongly coupled single-electron transistor

TL;DR

This paper derives a Lindblad-form master equation for charge qubit measurement by a strongly coupled single-electron transistor, analyzing measurement sensitivity, back-action, and conditions for near-ideal detection.

Contribution

It introduces a Lindblad-form master equation and quantum trajectory model for strong coupling regimes in SET-based charge qubit measurement, improving physical validity and analysis.

Findings

Strong coupling causes additional back-action beyond quantum limits.

In an asymmetric regime, the SET can nearly achieve ideal measurement conditions.

The model generalizes traditional concepts like measurement and decoherence times for strong responses.

Abstract

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 tunnelling 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.