Influence of External Fields and Environment on the Dynamics of Phase Qubit-Resonator System

TL;DR

This paper investigates how external electromagnetic fields and environmental factors influence the dynamics of a qubit-resonator system, deriving equations for the system's behavior and exploring measurement fidelity and state control.

Contribution

It introduces a comprehensive theoretical framework for analyzing qubit-resonator dynamics under external fields and bath interactions, including frequency renormalization and control of qubit states.

Findings

Resonator frequency is renormalized by qubit interaction.

Measurement fidelity depends on measurement time.

Qubit state relaxation can be controlled via drive parameters.

Abstract

We analyze the dynamics of a qubit-resonator system coupled with a thermal bath and external electromagnetic fields. Using the evolution equations for the set of Heisenberg operators, that describe the whole system, we derive an expression for the resonator field, accounting for the resonator-drive,-bath, and -qubit interaction. The renormalization of the resonator frequency, caused by the qubit-resonator interaction, is accounted for. Using solutions for the resonator field, we derive the equation describing qubit dynamics. The influence of the qubit evolution during the measurement time on the fidelity of a single-shot measurement is studied. The relation between the fidelity and measurement time is shown explicitly. Also, an expression describing relaxation of the superposition qubit state towards its stationary value is derived. The possibility of controlling this state, by varying the amplitude and frequency of drive, is shown.