Dynamical Symmetry and Generation of Squeezed States of Light

Using the Lie-algebraic approach, we develop the theory of generation of squeezed states of light in nonstationary parametric processes of the light interaction with a medium with the quadratic and quartic nonlinearities. The exact solution for the variance of the quadrature component of the field strength is obtained in the case of the quadratic parametric process with the SU(1, 1) dynamical symmetry. We show that decay of the field mode in this processes may have strong impact on squeezing. The solution for the standard deviation of the field strength in the case of the quartic parametric process with the approximated \({\mathcal{L}}_{5}\) dynamical symmetry is obtained in the first order of smallness with respect to the nonlinearity parameter.