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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum dynamics and statistics of two-coupled down-conversion processes

Ladislav Mišta, Jiří Herec, Viktor Jelínek, Jaroslav Řeháček, Jan Peřina

Published Mar 7, 2001• 1 citation
Publisher

Abstract

In the framework of the Heisenberg-Langevin theory the statistical effects arising from a mutual interaction of two non-degenerate down-conversion processes are investigated. Primarily, we focus on the possibility to control the intensity and statistical properties of the light generate din one nonlinear medium by the light entering the other one. We also show that the model discussed is an interesting generalization of the famous experiments by Zou, Wang, and Mandel on the induced coherence without induced emission.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

DOI
10.1117/12.417810

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 14, 1999•0 citations
In the framework of the Heisenberg-Langevin theory the statistical effects arising from a mutual interaction of two non-degenerate down-conversion processes are investigated. Primarily, we focus on the possibility to control the intensity and statistical properties of the light generate din one nonlinear medium by the light entering the other one. We also show that the model discussed is an interesting generalization of the famous experiments by Zou, Wang, and Mandel on the induced coherence without induced emission.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
In the framework of the Heisenberg-Langevin theory the dynamical and statistical effects arising from a mutual interaction of two non-degenerate down-conversion processes are investigated. Primarily, we focus on the possibility of controlling the intensity and statistical properties of the light generated in one nonlinear medium by the light entering the other one. Apart from this all-optical switching, behaviour reminiscent of the Zeno and anti-Zeno effects is examined. We also show that the model discussed is an interesting generalization of the famous experiments by Zou et al (Zou X Y, Wang L J and Mandel L 1991 Phys. Rev. Lett. 67 318) on induced coherence without induced emission.
A unified treatment of the description of the statistical dynamical properties of two-mode quadratic optical parametric processes with intense coherent or stochastic pumping (parametric amplification, frequency conversion, second subharmonic generation, etc. as special cases are involved) including the lossy mechanism is developed. The Heisenberg-Langevin equations are derived and their solutions are used to obtain the quantum characteristic functions and the corresponding quasidistributions. The Fokker-Planck equation approach is adopted as well and the equivalence of both the approaches is explicitly found.
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.
In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through non-degenerate optical parametric interaction. Main attention is paid to generation and transmission of non-classical light, based on a discussion of the squeezing phenomenon, the normalized second-order correlation function and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed with dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state |1〉 enters the first waveguide and the vacuume state |0〉 enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays a similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.
Nonlinear interaction of light with matter is described from the quantum-statistical point of view. The cases of two-photon absorption, Raman transition, sum-frequency generation, parametric amplification, and incoherent scattering are discussed. It is shown that the nonlinear optical effects depend strongly on the statistical properties of the light fields. The rate of nonlinear absorption, generation, and amplification is higher for chaotic than for coherent, and also higher for multimode than for single-mode pump fields. Measurements of the statistics of the output fields may yield information about the statistics of the input fields and the properties of the medium.
We examine phase properties of the contradirectional nonlinear asymmetric coupler with the second harmonic generation. We derive a phase distribution using the concept of phase space. An interesting behavior of the linear mode, namely bifurcation of the phase distribution and phase switching are demonstrated. It is shown that light initially in the coherent state approximately maintains its phase properties during amplification through its Poissonian photon-number statistics are not conserved.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.