Quantum Time-evolution in Qubit Readout Process with a Josephson Bifurcation Amplifier

TL;DR

This paper provides a quantum mechanical analysis of the Josephson bifurcation amplifier (JBA) used for superconducting qubit readout, highlighting how decoherence influences bifurcation and the measurement process.

Contribution

It introduces a quantum mechanical framework for analyzing JBA readout, including the effects of decoherence and the dynamics of qubit-probe entanglement during measurement.

Findings

Decoherence enables bifurcation in quantum cases.

Qubit-probe entanglement occurs at bifurcation.

Measurement timing depends on decoherence strength.

Abstract

We analyzed the Josephson bifurcation amplifier (JBA) readout process of a superconducting qubit quantum mechanically. This was achieved by employing numerical analyses of the dynamics of the density operator of a driven nonlinear oscillator and a qubit coupled system during the measurement process. In purely quantum cases, the wavefunction of the JBA is trapped in a quasienergy-state, and bifurcation is impossible. Introducing decoherence enables us to reproduce the bifurcation with a finite hysteresis. Moreover, we discuss in detail the dynamics involved when a qubit is initially in a superposition state. We have observed the qubit-probe (JBA) entangled state and it is divided into two separable states at the moment of the JBA transition begins. This corresponds to "projection". To readout the measurement result, however, we must wait until the two JBA states are macroscopically well separated. The waiting time is determined by the strength of the decoherence in the JBA.