  We demonstrate the generation of non-classical light by destructive
interference of identical Kerr squeezed states. Perfect pair-wise cancellation
of amplitudes that contribute to odd Fock states results in light with only
even Fock states, independent of the strength of the nonlinearity. The
observability of this effect is only limited by the quality of the
interferometer. In the low nonlinearity limit, the even-only state resembles a
squeezed vacuum state, yet the even-odd oscillations persist when the
nonlinearity is strong. The effect is also robust against deviations from the
optimum relative phase of the input Kerr-squeezed states.
