We show that the nonlinear response of a driven circuit quantum electrodynamics setup displays antiresonant multiphoton transitions, as recently observed in a transmon qubit device. By including photon leaking, we explain the lineshape by a perturbative and a semiclassical analysis. We derive a bistable semiclassical quasienergy surface whose lowest quasienergy eigenstate is squeezed, allowing for a squeezing-dependent local effective temperature. We study the escape dynamics out of the metastable state and find signatures of dynamical tunneling, similar as for the quantum Duffing oscillator.
@article{arxiv.0903.2338,
title = {Dynamical bistability in the driven circuit QED},
author = {V. Peano and M. Thorwart},
journal= {arXiv preprint arXiv:0903.2338},
year = {2015}
}