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Spatial distribution of quantum fluctuations in spontaneous down-conversion in realistic situations

Comparison between the stochastic approach and the Green’s function method

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Abstract.

We show that in the limit of negligible pump depletion, the spatial distribution of the quantum fluctuations in spontaneous parametric down-conversion can be computed for any shape of the pump beam by using the Green’s function method to linearize the quantum fluctuations, even for very low levels of the intensities measured on the pixels. The results are in complete agreement with stochastic simulations of the Wigner distribution. Both methods show specific quantum effects in realistic situations close to the experiments now in progress, like sub-shot noise correlation between opposite pixels in the far field.

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  20. Note that this property vanishes for higher gains: \(\tilde {C}_{\vec {r},\vec {r}} \) and \(\tilde {C}_{\vec {r},-\vec {r}} \) become almost equal for intensities of several tens of photons per pixel and \(\tilde {C}_{\vec {r},\vec {r}} \) becomes very slightly greater than \(\tilde {C}_{\vec {r},-\vec {r}} \) for intensities greater than 300 photons per pixel. This evolution confirms that quantum effects are more visible when thermal-like fluctuations are not too intense. It is not clear if the complete disappearance of quantum effects for high gains is physical or due to numerical accuracy problems. On the experimental side however, it is quite clear that the sub-shot noise level on the differences cannot be attained when the shot-noise fluctuations are very small compared to the thermal fluctuations

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Authors and Affiliations

  1. Laboratoire d’Optique P.M. Duffieux, Institut Femto ST, UMR 6174 du CNRS, Université de Franche-Comté, 25030, Besançon Cedex, France

    E. Lantz

  2. Laboratoire Kastler Brossel, UMR 8552 du CNRS, Université Pierre et Marie Curie, case 74, 75252, Paris Cedex 05, France

    N. Treps & C. Fabre

  3. INFM, Dipartimento di Scienze CC.FF.MM., Universitá dell’Insubria, Via Valleggio 11, 22100, Como, Italy

    E. Brambilla

Authors
  1. E. Lantz
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  2. N. Treps
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  3. C. Fabre
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  4. E. Brambilla
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Corresponding author

Correspondence to E. Lantz.

Additional information

Received: 15 January 2004, Published online: 23 March 2004

PACS:

42.65.Yj Optical parametric oscillators and amplifiers - 42.50.-p Quantum optics - 42.65.-k Nonlinear optics

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Lantz, E., Treps, N., Fabre, C. et al. Spatial distribution of quantum fluctuations in spontaneous down-conversion in realistic situations. Eur. Phys. J. D 29, 437–444 (2004). https://doi.org/10.1140/epjd/e2004-00040-4

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  • DOI: https://doi.org/10.1140/epjd/e2004-00040-4

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