Influence of external fields and environment on the dynamics of a phase-qubit–resonator system

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 * Corresponding author: gpb@lanl.gov 1 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.

Dynamics of a Phase Qubit-Resonator System: Requirements for Fast Nondemolition Readout of a Phase Qubit

“…As in our previous paper [9], we consider a flux-biased phase qubit embedded in a symmetric transmission line by a set of distributed inductances and capacitances. This is shown schematically in Fig.…”

“…The oscillations decay for times greater than 2/κ. Their influence on the measurement fidelity was analyzed in [9]. The total relaxation of the qubit can be described by taking into account the right-hand side of Eq.…”

“…After this, the cavitydrive resonant conditions are satisfied (ω d = ω r + χ), and the field amplitude, a(t), starts to grow. Using the approach of [9], we can analytically obtain an expression for the resonator field. With the initial (at t = t 0 ) value of a(t) given by steady-state term, Eq.…”

“…The analytical approach in Ref. [9] is based on a set of inequalities, where the indices i, j indicate the corresponding frequencies, ω q,r,d . The relations (2) indicate that all frequencies are close to each other.…”

“…The optimal choice of both the readout strategy and the setup parameters can be facilitated by means of theoretical description of the physical processes involved in the course of readout. In what follows, we use our recent approach [9] which makes it possible to obtain explicit expressions for the photon numbers and the measurement-induced relaxation rate of the qubit. We derive a set of inequalities which are required to provide a single-shot dispersive measurement, and we present examples of the qubit and resonator parameters.…”