Abstract

It is well known that parametric amplifiers create and destroy pairs of photons simultaneously, leading to nonclassical properties such as strong quantum correlations between the fields and squeezing.¹ We consider here a parametric interaction inside a cavity, exciting two modes symmetrically placed about a high carrier frequency. Inhomogeneous cavity losses are considered. Previous results have been obtained for the intracavity squeezing spectrum using phasespace methods based on the Wigner representation.² The quantum correlation properties of light generated by such processes have also been analyzed using an input-output theory.³ The main purpose of this work is to extend these previous results and examine new features arising from a detuning in frequency and an asymmetry in the losses. We derive the Quantum Langevin equations for the two-mode quadrature-phase amplitudes a, and α₂ proposed by Caves⁴ as the natural quantum mechanical operators for the modes. These amplitudes are the Fourier components of observables (quadratures) directly measured in phasesensitive schemes such as heterodyne detection.⁵ We use the input-output formalism to derive the spectra of the fluctuations inside and outside the cavity, for the parametric oscillator operating below threshold. We analyze in detail the combined effects of frequency detuning and asymmetry of the losses on the noise distribution in the transmitted fields. Particular attention is given to the degradation of noise reduction due to the asymmetry of the losses. We examine the filtering effect of the mirror on the inter-beam correlation. In this way a clear physical interpretation of the sensitivity of the Einstein-Podolsky-Rosen correlations on the nonhomogeneity of the losses can be obtained.

© 1994 IEEE