  We describe the creation of nonclassical states of microwave radiation via
ideal dichotomic single photon detection, i.e., a detector that only indicates
presence or absence of photons. Ideally, such a detector has a back action in
the form of the subtraction operator. Using the non-linearity of this back
action, it is possible to create a large family of nonclassical states of
microwave radiation, including squeezed and multi-component cat states,
starting from a coherent state. We discuss the applicability of this protocol
to current experimental designs of Josephson Photomultipliers (JPMs).
