Theory of weak continuous measurements in a strongly driven quantum bit

TL;DR

This paper develops a theoretical framework for understanding weak continuous measurements of a strongly driven superconducting qubit using a tank circuit, analyzing backaction effects and conditions for effective Rabi oscillation spectroscopy.

Contribution

It introduces a detailed theoretical model linking detector signals to qubit dynamics, including backaction effects, and identifies conditions for weak measurement of Rabi oscillations.

Findings

Voltage spectrum reveals Rabi oscillation frequency and decay rate.

Measurement efficiency and decoherence show resonant behavior near tank resonance.

Conditions for weak continuous measurement of flux qubits are established.

Abstract

Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector, namely, a spectrum of voltage fluctuations and an impedance, are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating wave approximations. Backaction effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about a frequency and a decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behaviour as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.