Some Integrable Systems in Nonlinear Quantum Optics

In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states related to these systems is constructed and described. Some applications are also presented.Comment: 27 page

Generalized coherent and squeezed states based on the h(1)⊗su(2)h(1) \otimes su(2) algebra

States which minimize the Schr\"odinger--Robertson uncertainty relation are constructed as eigenstates of an operator which is a element of the h(1) \oplus \su(2) algebra. The relations with supercoherent and supersqueezed states of the supersymmetric harmonic oscillator are given. Moreover, we are able to compute gneneral Hamiltonians which behave like the harmonic oscillator Hamiltonian or are related to the Jaynes--Cummings Hamiltonian.Comment: 42 pages, 10 figure