  The very small size of optical nonlinearities places wide ranging
restrictions on the types of novel physics one can explore. For an ensemble of
multi-level systems one can synthesize a large effective optical nonlinearity
using quantum coherence effects but such non-linearities are technically
extremely challenging to demonstrate at the single atom level. In this work we
describe how a single artificial multi-level Cooper Pair Box molecule,
interacting with a superconducting microwave coplanar waveguide resonator, when
suitably driven, can generate extremely large optical nonlinearities at
microwave frequencies, with no associated absorption. We describe how the giant
self-Kerr effect can be detected by measuring the second-order correlation
function and quadrature squeezing spectrum.
