Coherent States of Non-Linear Lie algebras: Application in Quantum Optics
1999
We present a general unified approach for finding the
coherent statesof 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 statesassociated with various
quantum opticalsystems.
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