Dynamics of coupled superconducting oscillators at high drive power: a time-coarse graining approach

We present a computationally efficient theoretical approach to accurately capture the dynamics of coupled quantum non-linear oscillators at high drive power embedded in an environment with a given spectral function. We take the point of view that the most resource-efficient approach should both require and provide no more and no less information than what can be measured in a particular experiment. We posit that one possible approach to do that is through time-coarse graining starting with the full Hamiltonian of the system and the environment with a well-characterized spectral function. A systematic derivation of effective (low frequency) quantum models is presented for basic models of interest in superconducting quantum systems. Specifically, we present the drive-dependent renormalized Hamiltonian and dissipative super operators of a driven Josephson non-linear oscillator coupled to a 50-ohm transmission line through a linear resonator.