Josephson bifurcation readout: beyond the monochromatic approximation

TL;DR

This paper investigates how higher harmonics influence Josephson bifurcation detectors, revealing their impact on dynamics and performance, which enhances understanding for quantum readout applications.

Contribution

It provides a quantitative analysis of higher harmonic effects in Josephson bifurcation circuits, extending beyond the monochromatic approximation to improve quantum detector modeling.

Findings

Higher harmonics significantly alter bifurcation characteristics.

Effects beyond the monochromatic approximation are quantitatively evaluated.

The circuit's sensitivity makes it suitable for quantum state detection.

Abstract

We analyze properties of bifurcation quantum detectors based on weakly nonlinear superconducting resonance circuits, in particular, with application to quantum readout. The developed quantitative description demonstrates strong influence of higher harmonics on their characteristics. While this effect is relevant for various circuits, including the conventional Josephson bifurcation amplifier and the parametrically driven circuit, we first focus on the period-doubling bifurcation under a force driving. This kind of bifurcation is due to nominally quadratic nonlinearity, which enables parametric down-conversion of the driving signal at nearly double resonance frequency to the basic mode. We analyze the effect of higher harmonics on the dynamics of the basic mode, inherent in a nonlinear circuit, which in our case is based on a Josephson junction with a sinusoidal current-phase relation as the origin of nonlinearity. We demonstrate that effects beyond the monochromatic approximation significantly modify the bare characteristics and evaluate their contribution. Due to high sensitivity of this circuit to small variations of parameters, it can serve as an efficient detector of the quantum state of superconducting qubits.