| We provide a theoretical model for a design involving a dc voltage biased Josephson Junction (JJ) that strongly drives a high quality factor microwave cavity via the ac Josephson effect. We explore the rich classical dynamics of the resultant nonlinear differential equation that categorizes the system. We contrast this with the quantum dynamics as derived by a model using the so called Rotating Wave Approximation Hamiltonian, and independently a Floquet analysis approach where no approximation is made on the Hamiltonian. We find that for certain parameters there is evidence of quantum activation, a process of over barrier transitions that stems from purely quantum mechanical considerations, and define an effective temperature that is non-zero even when coupled to a zero temperature bath. |
