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Optics Communications

Quantum phase fluctuations of coherent and thermal light coupled to a non-degenerate parametric oscillator beyond rotating wave approximation

Mohosin Alam, Swapan Kumar Mandal, Mohamed Ridza Wahiddin

Published Apr 15, 2017• 7 citations
Publisher
DOI
10.1016/j.optcom.2017.04.019

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Under the classical (strong) pump condition, the Hamiltonian involving the signal and the idler modes of a non-degenerate 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.
The aim of this paper is to investigate dynamical properties of a harmonic oscillator coupled to a non-equilibrium bath without the rotating wave approximation. At first, we investigate the theory of this model and obtain the Heisenberg equations of motion for the oscillator and bath annihilation operators in the absence and in the presence of a rotating wave approximation. Then, we obtain the fluctuation and fluctuation-dissipation relations in the absence and in the presence of a rotating wave approximation for the non-equilibrium bath annihilation operator, respectively. After that, we study the decay of system modes using the Wigner-Weisskopf approximation. Finally, we calculate the time-dependent spectrum of a cavity field mode coupled to a non-equilibrium reservoir. We show that even under the condition in which the RWA is considered to be valid (weak interaction), there are significant effects of virtual-photon field on the diffusion coefficient, the energy density, line width and the shift frequency.
The degenerate parametric oscillator is an important source of squeezed light. If the pump mode is adiabatically eliminated, its operation is governed by two dimensionless parameters: the pump parameter λ and the coupling constant g. The pump parameter controls the threshold behavior predicted by semiclassical theory (threshold is reached for λ = 1). The coupling constant g determines the strength of the quantum fluctuations. The optical parametric oscillators used to generate squeezed light have g ~ 10–4 ≪ 1.1 Therefore, in these systems the quantum fluctuations only produce very small perturbations about semiclassical states. We have recently shown how the steady state of the degenerate parameter oscillator changes as a function of coupling strength.2 In the strong coupling limit, major departures from semiclassical states occur; for g2 ≫ 1 and 2λ2/g2 ≪ 1 the steady state approches the coherent state superposition | ψ + 〉 = | λ / g 〉 + | − λ / g .