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Quantum properties of tranverse pattern formation in second-harmonic generation

AuthorsBache, Morten; Scotto, Pierre; Zambrini, Roberta ; San Miguel, Maxi ; Saffman, Mark
Keywords[PACS] Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements
[PACS] Quantum fluctuations, quantum noise, and quantum jumps
[PACS] Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics
Issue Date19-Jul-2002
PublisherAmerican Physical Society
CitationPhysical Review A 66(1): 013809 (2002)
AbstractWe 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.
Description17 pages, 17 figures.-- PACS nrs.: 42.50.Dv, 42.50.Lc, 42.65.Sf.-- ArXiv pre-print available at: http://arxiv.org/abs/quant-ph/0202167
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevA.66.013809
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