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We demonstrate that superpositions of coherent and displaced Fock states,also referred to as generalized Schr\"odinger cats cats, can be created byapplication of a nonlinear displacement operator which is a deformed version ofthe Glauber displacement operator. Consequently, such generalized cat statescan be formally considered as nonlinear coherent states. We then show thatGlauber-Fock photonic lattices endowed with alternating positive and negativecoupling coefficients give rise to classical analogs of such cat states. Inaddition, it is pointed out that the analytic propagator of these deformedGlauber-Fock arrays explicitly contains the Wigner operator opening thepossibility to observe Wigner functions of the quantum harmonic oscillator inthe classical domain.

Generalized Schr\"odinger cat states and their classical emulation