dorsal/arxiv
View SchemaQuantum properties of transverse pattern formation in second-harmonic generation
| Authors | M. Bache, P. Scotto, R. Zambrini, M. San Miguel, M. Saffman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202167 |
| URL | https://arxiv.org/abs/quant-ph/0202167 |
| DOI | 10.1103/PhysRevA.66.013809 |
| Journal | Phys. Rev. A 66, 013809 (2002) |
Abstract
We investigate the spatial quantum noise properties of the one dimensional transverse pattern formation instability in intra-cavity 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.
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"abstract": "We investigate the spatial quantum noise properties of the one dimensional\ntransverse pattern formation instability in intra-cavity second-harmonic\ngeneration. The Q representation of a quasi-probability distribution is\nimplemented in terms of nonlinear stochastic Langevin equations. We study these\nequations through extensive numerical simulations and analytically in the\nlinearized limit. Our study, made below and above the threshold of pattern\nformation, is guided by a microscopic scheme of photon interaction underlying\npattern formation in second-harmonic generation. Close to the threshold for\npattern formation, beams with opposite direction of the off-axis critical wave\nnumbers are shown to be highly correlated. This is observed for the fundamental\nfield, for the second harmonic field and also for the cross-correlation between\nthe two fields. Nonlinear correlations involving the homogeneous transverse\nwave number, which are not identified in a linearized analysis, are also\ndescribed. The intensity differences between opposite points of the far fields\nare shown to exhibit sub-Poissonian statistics, revealing the quantum nature of\nthe correlations. We observe twin beam correlations in both the fundamental and\nsecond-harmonic fields, and also nonclassical correlations between them.",
"arxiv_id": "quant-ph/0202167",
"authors": [
"M. Bache",
"P. Scotto",
"R. Zambrini",
"M. San Miguel",
"M. Saffman"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.013809",
"journal_ref": "Phys. Rev. A 66, 013809 (2002)",
"title": "Quantum properties of transverse pattern formation in second-harmonic generation",
"url": "https://arxiv.org/abs/quant-ph/0202167"
},
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