Generation of squeezed Schr\"odinger cat states with an operation allowing iterative growth

We present what is to our knowledge the first implementation of a Schr"odinger cat states “breeding” operation, which allows an iterative growth of these states. We thus report the experimental generation of a squeezed Schr"odinger cat state from two single photon Fock states, which can be seen as cat states with zero amplitude. These Fock states are mixed on a symmetrical beamsplitter and the generation is heralded by a homodyne measurement in one of the two output arms. The output state has a fidelity of 61% with an even squeezed Schr"odinger cat state of amplitude $\alpha =1.63$. This hybrid operation opens up new prospects in quantum optics as the protocol depicted here can be iterated in order to produce new kind of mesoscopic states.