Dynamical bistability in the driven circuit QED

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 to de. ne 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. Copyright (C) EPLA, 2010