Generation of macroscopic superpositions of field states by nonlinear processes

The fourth lesson addressed the problem of non-linear splitters in quantum optics. After noting that the photon distribution achieved in the final channels of a linear splitter did not in any case allow the realization of a mesoscopic superposition of the Schrödinger "cat" type, we showed that a simple modification of the blade, transforming it into a nonlinear device "decomposing" a photon into several final photons whose sum of frequencies is equal to that of the initial particle, allowed the realization of coherent superpositions of several photons in different modes. By combining two non-linear blades in a non-linear Mach-Zehnder interferometer, we showed that these superpositions had interferometric signatures different from that given by a single particle. Finally, we described a practical realization of such non-linear blades in an experiment involving a trapped ion. In this case, the photons are replaced by phonons, excitations of the ion's vibrational modes. These phonons can be used to perform the analogue of a non-linear Mach-Zehnder experiment, and to observe the characteristic signals of superpositions involving two or three phonons.