Quantum-interference effects on the superposition of N displaced number states

We describe properties of a quantum system prepared in a superposition of N displaced number states, with emphasis on the interference effects among the state components. Explicit expressions for wavefunctions in the coordinate and Fock-state representations, photon number distribution, variances and quantum correlation coefficient of the quadrature operators, and quasiprobability distributions are calculated in detail. Nonclassical effects due to such interference and the analogy with diffraction patterns arising in an N slit Young-type experiment are the main results in the present work. In particular, we show that interference and correlation effects in phase space are connected with the nondiagonal term of the quasiprobability distributions, providing further insight into the phenomenon.