Sideband transitions in a two-mode Josephson circuit driven beyond the rotating wave approximation

TL;DR

This paper investigates the limitations of the rotating wave approximation in strongly driven two-mode Josephson circuits, revealing that it underestimates transition amplitudes but still accurately predicts overall dynamics at high drive strengths.

Contribution

It provides experimental, numerical, and analytical insights into the breakdown of RWA in large detuning and strong driving regimes, with a focus on two-photon sideband transitions.

Findings

RWA fails to accurately predict sideband transition amplitudes under strong driving.

Breakdown of RWA does not qualitatively change the system dynamics at high drive strengths.

Enhanced coupling rates are observed beyond RWA predictions.

Abstract

Driving quantum systems periodically in time plays an essential role in the coherent control of quantum states. The rotating wave approximation (RWA) is a good approximation technique for weak and nearly-resonance driven fields. However, these experiments sometimes require large detuning and strong driving fields, for which the RWA may not hold. In this work, we experimentally, numerically, and analytically explore strongly driven two-mode Josephson circuits in the regime of strong driving and large detuning. Specifically, we investigate beam-splitter and two-mode squeezing interaction between the two modes induced by driving a two-photon sideband transition. Using numerical simulations, we observe that the RWA is unable to correctly capture the amplitude of the sideband transition rates. We verify this finding using an analytical model that is based on perturbative corrections. We find that the breakdown of the RWA in the regime studied does not lead to qualitatively different dynamics, but gives the same results as the RWA theory at higher drive strengths, enhancing the coupling rates compared to what one would predict. This is an interesting consequence compared to the carrier transition case, where the breakdown of the RWA results in qualitatively different time evolution of the quantum state. Our work provides an insight into the behavior of time-periodically driven systems beyond the RWA. We also provide a robust theoretical framework for including these findings in the calculation and calibration of quantum protocols in circuit quantum electrodynamics.