  We explore the joint activated dynamics exhibited by two quantum degrees of
freedom: a cavity mode oscillator which is strongly coupled to a
superconducting qubit in the strongly coherently driven dispersive regime.
Dynamical simulations and complementary measurements show a range of parameters
where both the cavity and the qubit exhibit sudden simultaneous switching
between two metastable states. This manifests in ensemble averaged amplitudes
of both the cavity and qubit exhibiting a partial coherent cancellation.
Transmission measurements of driven microwave cavities coupled to transmon
qubits show detailed features which agree with the theory in the regime of
simultaneous switching.
