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Journal of Modern Optics

Quantum Statistical Properties of Coupled Nonlinear Oscillators with Losses

Jan Peřina, R. Horák, Z. Hradil, Concita Sibilia, M. Bertolotti

Published May 1, 1989• 11 citations
Publisher

Abstract

The statistical properties of two coupled nonlinear oscillators including losses are discussed using the statistics for the generalized superposition of coherent fields and quantum noise. Exact and approximate formulae for squeezing of vacuum fluctuations are derived. The photon statistics are shown to be Poissonian from the nonlinear dynamics of the lossless case. Non-classical behaviour is degraded by noise.

DOI
10.1080/09500348914550681

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The statistical properties of two coupled nonlinear oscillators including losses are discussed using the statistics for the generalized superposition of coherent fields and quantum noise. Exact and approximate formulae for squeezing of vacuum fluctuations are derived. The photon statistics are shown to be Poissonian from the nonlinear dynamics of the lossless case. Non-classical behaviour is degraded by noise.
Statistical properties of optical fields in nonlinear couplers composed of two waveguides in which Raman or Brillouin processes (with classical pumping) are in operation and which are mutually connected through the mutual Stokes and/or anti-Stokes linear interactions are investigated within the framework of a generalized superposition of coherent fields and quantum noise. Heisenberg equations describing the couplers are solved both analytically under special conditions and numerically in general cases. Regimes for nonclassical properties of optical fields, such as sub-Poissonian photon-number statistics, negative reduced moments of integrated intensity and squeezing of quadrature fluctuations are discussed for the cases of single and compound fields. General results are compared with those from the short-length approximation.
The statistical properties of nonlinear oscillators modeling dissipative forward four-wave mixing are investigated, adopting the Fokker-Planck equation approach. The photon statistics are shown to be insensitive to the nonlinearities and are formulated in terms of the superposition of coherent and chaotic fields. The only approximation in describing the squeezing properties consists in the way of including thermal noise. The effect of the initial coherent amplitudes, that of the interplay of the coupling constants, and that of the reservoir on the squeezing properties are studied. An interesting connection between the revivals of coherent amplitudes and squeezing is pointed out.
We derive the quantum statistical properties of light beams involved in an asymmetric nonlinear coupler composed of a linear waveguide and a nonlinear waveguide operating using second harmonic generation. Examining quadrature and integrated intensity fluctuations, photon number distribution, reduced factorial moments and the uncertainty product, we demonstrate non-classical behaviour of single and compound modes. We show that squeezing of vacuum fluctuations, sub-Poissonian photon statistics and oscillations in photon number distribution created by nonlinear dynamics can be transferred to the linear signal mode. Also effects of non-classical incident beams and smoothing effects of external noise are demonstrated.
We investigate nonlinear couplers whose operation is based on Raman or Brillouin scattering. A quantum approach is used. Strong coherent laser pumping is assumed and linearized Heisenberg-Langevin equations of motion are solved. The influence of linear coupling constants, losses and phase mismatches on the dynamical behaviour of the coupler is discussed. Quantum statistical properties of optical modes involved in the interaction are investigated within the framework of the generalized superposition of coherent signal and quantum noise. Most attention is devoted to the possibility of generation of non-classical light. It is shown that such light can be generated only in compound modes according to our model and influence of various parameters on the generation is discussed. Optimal conditions for the generation of squeezed light are found.