Resonant effects in the strongly driven phase-biased Cooper-pair box

Abstract

We study the time-averaged upper level occupation probability in a strongly driven two-level system, particularly its dependence on the driving amplitude x₀ and frequency ω and the energy level separation ∆E. In contrast to the case of weak driving (x₀ ≪ ∆E), when the positions of the resonances almost do not depend on x₀, in the case of the strong driving (x₀ ~ ∆E) their positions are strongly amplitude dependent. We study these resonances in the concrete system — the strongly driven phase-biased Cooper-pair box, which is considered to be weakly coupled to the tank circuit.