Quantum properties of transverse pattern formation in second-harmonic generation

M. Bache, P. Scotto, R. Zambrini, M. San Miguel, and M. Saffman
Phys. Rev. A 66, 013809 – Published 19 July 2002
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Abstract

We investigate the spatial quantum noise properties of the one-dimensional transverse pattern formation instability in intracavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second-harmonic field, and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.

  • Received 21 February 2002

DOI:https://doi.org/10.1103/PhysRevA.66.013809

©2002 American Physical Society

Authors & Affiliations

M. Bache1,2,3, P. Scotto1, R. Zambrini1, M. San Miguel1, and M. Saffman4

  • 1Instituto Mediterráneo de Estudios Avanzados, IMEDEA (SCSIC-UIB), Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain
  • 2Optics and Fluid Dynamics Department, Risø National Laboratory, Postbox 49, DK-4000 Roskilde, Denmark
  • 3Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800 Lyngby, Denmark
  • 4Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706

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Vol. 66, Iss. 1 — July 2002

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