  I analyze a scheme that is capable of producing large Kerr nonlinearities on
cavity-atom polaritons in a cavity QED system consisting of multiple
three-level atoms confined in a cavity mode. A weak control laser coupled to
the atoms from free space induces destructive quantum interference in the
polariton excitation of the coupled cavity-atom system and creates large Kerr
nonlinearities on the intra-cavity light field. The scheme can be used for
optical switching or cross-phase modulation of the cavity-atom polariton at
ultra-low light levels, which may be useful for applications in quantum state
manipulation in cavity QED, quantum measurements, and quantum logic gates.
