  We develop a technique for generating multi-photon nonclassical states via
interference between coherent and Fock states using quantum catalysis. By
modulating the coherent field strength, the number of catalyst photons and the
ratio of the beam splitter upon which they interfere, a wide range of
nonclassical phenomena can be created, including squeezing of up to 1.25 dB,
anti- and super-bunched photon statistics and states exhibiting over 90%
fidelity to displaced coherent superposition states. We perform quantum
catalysis experimentally, showing tunability into the nonclassical regime. Our
protocol is not limited by weak nonlinearities that underlie most known
strategies of preparing multi-photon nonclassical states. Successive iterations
of this protocol can lead to direct control over the weights of higher-order
terms in the Fock basis, paving the way towards conditional preparation of
"designer" multi-photon states for applications in quantum computation,
communication and metrology.
