Equation of motion approach to black-box quantization: Taming the multimode Jaynes-Cummings model
Fabian Hassler, Jakob Stubenrauch, Alessandro Ciani · Physical review. B./Physical review. B · 2019
An accurate modeling of a Josephson junction that is embedded in an arbitrary environment is of crucial importance for qubit design. We present a formalism to obtain a Lindblad master equation that describes the evolution of the system. As the qubit degrees of freedom oscillate with a well-defined frequency ${\ensuremath{\omega}}_{q}$, the environment only has to be modeled close to this frequency. We show that this goal, differently from alternative approaches, can be achieved by modeling the environment with only a few degrees of freedom. We treat the example of a transmon qubit coupled to a stripline resonator. We derive the parameters of a dissipative single-mode Jaynes-Cummings model starting from first principles. We show that the leading contribution of the off-resonant modes is a correlated decay process involving both the qubit and the resonator mode. In particular, our results show that the effect of the off-resonant modes in the multimode Jaynes-Cummings model is perturbative in $1/{\ensuremath{\omega}}_{q}$.