Abstract
In this paper we will study the statistical properties of a generalized superposition of two displaced number states of the form, [Formula: see text] with a phase difference of φ between them. A particular case of this state is obtained when we consider n1=n2=n and α1=-α2=α, which we will call even and odd displaced number state. It will be shown that they are the generalization of the even and odd coherent states. The generation of this states, based on the dispersive interaction with a two-level atom, will also be discussed.
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