On the stable evolution of squeezed and correlated states

It is shown that the stable evolution equations for the squeezed and correlated states (SS and CorS) in the form of H_w × SU (l.l)-coherent states with maximal symmetry are classical Hamiltonian equations with a Kaehler symplectic 2-form of Onofri type. The evolution of the second momenta of the Hermitian quadratures of the boson operator is described by canonical equations. The general form of the Hamiltonian which correlates without squeezing is found and the connection of the stable evolution of SS and CorS with the existence of linear integrals of motion is pointed out.Presented at the International Workshop on Squeezed and Correlated States in Quantum Optics, Moscow, December 3–7, 1990.