FLUCTUATIONS AND SQUEEZING IN ONE-MODE AND 2-MODE OF 2 COUPLED OSCILLATORS

The investigation of one- and two-mode quantum fluctuations and squeez ing in coupled oscillators is a current matter in the recent literatur e. The coupling model Hamiltonian has the usual form V = i ($) over ba r h gamma(alpha(1) alpha(2) - alpha(1)(dagger) alpha(2)(dagger)), wher e alpha(i), alpha(i)(dagger), are the traditional ladder operators. He re we will extend this model by including the interaction Hamiltonian V' = i ($) over bar h gamma'(alpha(1) alpha(2)(dagger) - alpha(1)(dagg er) alpha(2) ) to investigate those fluctuations in the scenery of two coupled oscillators in the controlled presence of the RWA terms. Part icular cases in the literature are obtained from this extended model f or gamma much greater than gamma', gamma much less than gamma' and gam ma = gamma'. For arbitrary values of gamma and, gamma' we obtain exact results for fluctuations in quadrature-phase amplitudes, for one- and two-mode oscillations, which are exhibited in several plots for diffe rent values of the involved parameters.