The essence of the rotating wave approximation (RWA) is to eliminate the non-conserving energy terms from the interaction Hamiltonian. The cost of using RWA is heavy if the frequency of the input radiation field is low (e.g. below optical region). The well known Bloch-Siegert effect is the out come of the inclusion of the terms which are normally neglected under RWA. We investigate the fluctuations of the quantum phase of the coherent light and the thermal light coupled to a nondegenerate parametric oscillator (NDPO). The Hamiltonian and hence the equations of motion involving the signal and idler modes are framed by using the strong (classical) pump condition. These differential equations are nonlinear in nature and are found coupled to each other. Without using the RWA, we obtain the analytical solutions for the signal and idler fields. These solutions are obtained up to the second orders in dimensionless coupling constants. The analytical expressions for the quantum phase fluctuation parameters due to Carruther's and Nieto are obtained in terms of the coupling constants and the initial photon numbers of the input radiation field. Moreover, we keep ourselves confined to the Pegg-Barnett formalism for measured phase operators.With and without using the RWA, we compare the quantum phase fluctuations for coherent and thermal light
Under the classical (strong) pump condition, the Hamiltonian involving the signal and the idler modes of a nondegenerate parametric oscillator is exhibited. Without using the usual rotating wave approximation (RWA), the analytical solutions of the field operators are used to investigate the antibunching of photons of the input radiation field coupled to the non-degenerate parametric oscillator. By using the symbolic calculation, the antibunching of photons for both the signal and idler modes are investigated. In particular, the effects of the inclusion of rotating wave approximated terms on the antibunching of photons are clearly indicated. To substantiate the analytical results, the temporal evolution of signal photon and idler photons , and the antibunching effects of the signal and idler modes are investigated numerically by using the QuTip 3.1.0. The exact numerical results obtained by QuTip 3.1.0 matches extremely well with those of the analytical results. The present article and hence the analytical method might be of use for investigating the situations of having ultra-strongly and deep-strongly coupled systems where the possibilities of using RWA is completely ruled out.
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