Polynomial deformations of the Lie algebrasl(2) in problems of quantum optics

V. P. Karassiov

Thomas Quella

Based on the rational R -matrix of the supersymmetric sl (2,1) matrix difference equations are solved by means of a generalization of the nested algebraic Bethe ansatz. These solutions are shown to be of highest weight with respect to the underlying graded Lie algebra structure.

Jules Beckers

V. Sunilkumar, Bindu A. Bambah, R. Jagannathan +2 more

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

V. P. Karassiov

V. Sunilkumar, Bindu A. Bambah, R. Jagannathan +2 more

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.