ar X iv : q ua nt - p h / 99 07 07 5 v 1 2 3 Ju l 1 99 9 Coherent States of Non - Linear Lie algebras : Applications in Quantum Optics

We present a general unified approach for finding the coherent states 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 non compact cases, to obtain the annihilation operator coherent states, by finding the canonical conjugates of these operators. Generalized coherent states, in the Perelomov sense also follow from this construction. This allows us to explicitly construct coherent states associated with various quantum optical systems.