  Large optical nonlinearities can have numerous applications, ranging from the
generation of cat-states for optical quantum computation, through to quantum
sensing where the sensitivity exceeds Heisenberg scaling in the resources.
However, the generation of ultra-large optical nonlinearities has proved
immensely challenging experimentally. We describe a novel protocol where one
can effectively generate large optical nonlinearities via the conditional
application of a linear operation on an optical mode by an ancilla mode,
followed by a measurement of the ancilla and corrective operation on the probe
mode. Our protocol can generate high quality optical Schr{\"{o}}dinger cat
states useful for optical quantum computing and can be used to perform sensing
of an unknown rotation or displacement in phase space, with super-Heisenberg
scaling in the resources. We finally describe a potential experimental
implementation using atomic ensembles interacting with optical modes via the
Faraday effect.
