Coherent states of nonlinear algebras: applications to quantum optics

We present a general unified approach for finding the coherent stares (CSs) of polynomially deformed algebras such as the quadratic and Higgs algebras , which are: relevant for various multiphoton processes in quantum optics. We give a general procedure: to map these deformed algebras to appropriate Lie algebras. This is used, for the noncompact cases, to obtain the annihil ation operator eigenstates, by finding the canonical conjugates of these op erators. Generalized CSs, in the Perelomov sense, also follow from this con struction. This allows us to explicitly construct CSs associated with vario us quantum optical systems.