Abstract: We present applications of parametric (two-photon) driving of a cavity in a generic cavity QED setup, which can be used to exponentially enhance the light-matter coupling. This can take a weakly coupled system into the strong coupling regime (where the coupling exceeds dissipative rates) and even the ultra-strong coupling regime (where the coupling is comparable to the cavity frequency). As an example, we show how this allows one to use a weak-coupling system to adiabatically prepare the highly entangled ground state of the ultra-strong coupling system. Furthermore, we show that by adding local Kerr nonlinearities to parametrically driven cavities one can stabilize an entangled cat-state between the cavities.