Generating non-classical light inside an optical cavity by depositing photons

The creation of non-classical states of light is an interesting problem, that we solve sending atoms through an optical cavity. We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measured in one of the Schmidt states, producing a multiphoton process (in the sense that can add or annihilate more photons than a single transition allows), i.e. adding or subtracting several photons from the cavity field. By plotting the quadratures and the Husimi Q-function, we also show that the non-classical state produced by such measurements is a squeezed state.