Sculpturing coherent states to get highly excited Fock states for stationary and travelling fields

An adapted sequential application of dispersive atom-field interaction is used to engineer a field in a highly excited Fock state. A few atoms are used to group into a number component all photons inside a microwave cavity which initially contains a coherent state. The scheme differs from those adding photons to an empty cavity via successive passage of resonant atoms. A conveniently equipped sequence of Mach-Zehnder interferometers is found to be the complementary scheme, extending the result for (optical) travelling waves.