Abstract

The production and detection of non-classical light continues to be a topic of interest to quantum optics. The quantum-mechanical superposition states (Schrodinger-Cat-like states) [1] are one of the non-classical states of light that is of great current interest. We consider a double resonant third harmonic generation in which three photons of frequency ω₁ in the fundamental mode a, can annihilate to produce a photon with the frequency ω₂=3ω₁ in the third harmonic mode a₂. The fundamental mode is resonantly driven by an external classical field. In this paper the dynamics of fluctuations of photon number and phases is investigated for process of the third harmonic generation. With this purpose in the positive P- representation we simulate the Langevin equations of an optical system. The third harmonic, in difference from process of the third subharmonic, for amplitude of fields has one classical solution which above a bifurcation point of the optical system becomes unstable. The system in this domain has only quantum solutions and is a macroscopic quantum object. For the fundamental mode and third harmonic for large times a superposition state will be realized. In difference from process of the second subharmonic [2], the quantum superposition state can be obtained in the case of a small nonlinearity. The density of joint distribution of photon number and phase of the fundamental mode and third harmonic are shown in Fig. a and b, respectively. The following values of parameters are used for calculations: (χ/γ)² = 10^–9 ε= 380, where χ is the resulting coupling constant proportional to the third-order susceptibility χ⁽³⁾, ε is the scaled amplitude of the driving field, γ is the cavity damping constant. At these values the critical perturbation is ε_cr ≈ 270.

© 1998 IEEE