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.
Highlights
Time-periodic driving is a prominent technique for the in situ coherent control of quantum dynamical processes
Our findings indicate that the rotating-wave approximation (RWA) is clearly violated, and significantly underestimates the mode frequency shifts and the sideband transition rates for a known driving strength, the breakdown of the RWA does not result in qualitatively different behavior but instead its effects in our measurements can be reproduced by the RWA theory using a larger drive field
Over the entire range of the driving amplitudes in this work, our theoretical, numerical, and experimental values agree with each other, which suggests that the faithful quantitative estimation of sideband transition rates is possible
Summary
Time-periodic driving is a prominent technique for the in situ coherent control of quantum dynamical processes. As long as the drive is weak enough and nearly resonant with the quantum state transition of a target observable, the rotating-wave approximation (RWA) may provide a good estimate of the dynamics [3,4] It is, necessary to understand the physics of quantum systems beyond the RWA from both a fundamental and a practical perspective. Our findings indicate that the RWA is clearly violated, and significantly underestimates the mode frequency shifts and the sideband transition rates for a known driving strength, the breakdown of the RWA does not result in qualitatively different behavior but instead its effects in our measurements can be reproduced by the RWA theory using a larger drive field. The confirmation of a breakdown of the RWA is only possible to observe experimentally in an accurate independent calibration of the drive field, our results show the importance of including counter-rotating terms for accurate calculations of the sideband transition rates
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