Analytical model of the readout power and SQUID hysteresis parameter dependence of the resonator characteristics of microwave SQUID multiplexers

TL;DR

This paper presents an analytical model for understanding how readout power and SQUID hysteresis influence the resonator characteristics in microwave SQUID multiplexers, validated by experimental data.

Contribution

The paper introduces a new analytical model that accurately describes the dependence of resonator characteristics on readout power and hysteresis, extending existing models.

Findings

Model aligns with existing models at low readout powers

Valid for hysteresis parameters $eta_{L} < 0.6$

Experimental results agree with model predictions

Abstract

We report on the development of an analytical model describing the readout power and SQUID hysteresis parameter dependence of the resonator characteristics used for frequency encoding in microwave SQUID multiplexers. Within the context of this model, we derived the different dependencies by analyzing the Fourier components of the non-linear response of the non-hysteretic rf-SQUID. We show that our model contains the existing model as a limiting case, leading to identical analytical expressions for small readout powers. Considering the approximations we made, our model is valid for rf-SQUID hysteresis parameters $\beta_{\mathrm{L}} < 0.6$ which fully covers the parameter range of existing multiplexer devices. We conclude our work with an experimental verification of the model. In particular, we demonstrate a very good agreement between measured multiplexer characteristics and predictions based on our model.