Fluctuations and squeezing in one- and two-mode of two coupled oscillators

Summary

The investigation of one- and two-mode quantum fluctuations and squeezing in coupled oscillators is a current matter in the recent literature. The coupling model Hamiltonian has the usual formV=i▄γ(a ₁a₂-a ^†₁ a ^†₂ ), wherea _i,a ^†_i , are the traditional ladder operators. Here we will extend this model by including the interaction HamiltonianV′=i▄γ′(a ₁a ^†₂ -a ^†₁ a₂) to investigate those fluctuations in the scenery of two coupled oscillators in the controlled presence of the RWA terms. Particular cases in the literature are obtained from this extended model for γ≫γ′ γ≪γ′ and γ=γ′. For arbitrary values of γ and γ′ we obtain exact results for fluctuations in quadrature-phase amplitudes, for one- and two-mode oscillations, which are exhibited in several plots for different values of the involved parameters.