Quantum trajectories for the realistic measurement of a solid-state charge qubit

TL;DR

This paper develops a realistic quantum trajectory model for continuous measurement of a solid-state charge qubit, incorporating noise and filtering effects of the measurement apparatus, extending previous photodetector models to solid-state detectors.

Contribution

It introduces a generalized quantum trajectory framework for solid-state measurements, accounting for realistic detector effects like noise and filtering, which was not previously modeled.

Findings

Derived stochastic equations for realistic quantum trajectories.

Applied the theory to a low transparency quantum point contact.

Discussed applications and relation to prior models.

Abstract

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman and H. Mabuchi, Phys. Rev. A_65_ 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the ``realistic quantum trajectories'' of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.