Current definitions of both squeezing operator and squeezed vacuum state are critically examined on the grounds of consistency with the underlying su(1,1) algebraic structure. Accordingly, the generalized coherent states for su(1,1) in its Schwinger two-photon realization are proposed as squeezed states. The physical implication of this assumption is that two additional degrees of freedom become available for the control of quantum optical systems. The resulting physical predictions are evaluated in terms of quadrature squeezing and photon statistics, while the application to a Mach-Zehnder interferometer is discussed to show the emergence of nonclassical regions, characterized by negative values of Mandels parameter, which cannot be anticipated by the current formulation, and then outline future possible use in quantum technologies.
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