Bistability and Critical Slowing Down in Superconducting Circuits

We carry out an experimental and numerical examination of bistability and critical slowing down in the strongly driven non-linear regime of circuit QED. The system under study is a 3D microwave cavity coupled to a transmon qubit. By measuring the response of the cavity to a step function drive pulse, we see that in the bistable regime the time required for the system to reach equilibrium is far longer than both the cavity and qubit relaxation times. We observe that this equilibration time saturates at high drive powers. Through careful modelling we are able to attribute this saturation to phase noise of the transmon. In addition we demonstrate that the equilibration time is highly sensitive to the temperature of the cavity.