Recently there is a rise of interest in optical systems displaying non classical features in the spatial domain. For example the possibility of amplifying a faint coherent image preserving the signal to noise ratio by means of a phase-sensitive parametric amplifier has been recently demonstrated (see e.g. [1]). The physical process we consider, parametric down conversion in a crystal with a (2) nonlinearity, is a good candidate to display such a kind of phenomena since its large amplification bandwidth leads to quantum entanglement between a large number of spatial modes of the optical field. The observation of such a spatial quantum correlation effects is the aim of an experiment presently performed at the University of Como under the direction of Prof. P. Ditrapani in the framework of the E.C. project QUANTIM (quantum images), in which we are involved. We consider here the spontaneously down-converted field that is emitted by the amplifier even when no signal field is injected. In this case, phase-matching conditions determine the angular distribution and the frequency spectrum of the emitted field. The signal and idler photons generated in this process are highly correlated one to each other and close to the degenerate frequency they are emitted almost symmetrically with respect to the system axis because of momentum conservation. As a consequence, intensity correlations are observable in the far field when one considers symmetrical detection areas; more precisely, it has been possible to demonstrate analytically that almost complete noise reduction in the subtracted signals measured by two identical detectors can be achieved [2]. The theoretical model that we have developed includes both diffraction and linear dispersion of the signal field. However, all analytical results have been obtained within the perfectly monochromatic plane wave pump approximation. In order to obtain a more realistic description of the system we have also developed a numerical model which includes the effects of the finite size of the pump beam profile and its finite frequency bandwidth. It is important to investigate how these features affects the spatial quantum correlation phenomena predicted by the theory within the plane wave pump approximation, also in view to identify the better conditions under which these correlations can be observed in the experiment. Moreover, a stochatic method has been implemented in order to evaluate the intensity correlation function and the amount of intensity squeezing which can be achieved. [1] Quantum aspects of imaging, A.Gatti, E.Brambilla, L.A.Lugiato and M.Kolobov J. Opt. B, Quant. and Semiclass. Opt. 2, 196 (2000) [2] Quantum Entangled Images, A. Gatti, E. Brambilla, L.A. Lugiato and M.I. Kolobov, Phys. Rev. Lett. 83, 1763 (1999)
Numerical model for spontaneous down-conversion in atravelling-wave parametric amplifier
BRAMBILLA, ENRICO;
2002-01-01
Abstract
Recently there is a rise of interest in optical systems displaying non classical features in the spatial domain. For example the possibility of amplifying a faint coherent image preserving the signal to noise ratio by means of a phase-sensitive parametric amplifier has been recently demonstrated (see e.g. [1]). The physical process we consider, parametric down conversion in a crystal with a (2) nonlinearity, is a good candidate to display such a kind of phenomena since its large amplification bandwidth leads to quantum entanglement between a large number of spatial modes of the optical field. The observation of such a spatial quantum correlation effects is the aim of an experiment presently performed at the University of Como under the direction of Prof. P. Ditrapani in the framework of the E.C. project QUANTIM (quantum images), in which we are involved. We consider here the spontaneously down-converted field that is emitted by the amplifier even when no signal field is injected. In this case, phase-matching conditions determine the angular distribution and the frequency spectrum of the emitted field. The signal and idler photons generated in this process are highly correlated one to each other and close to the degenerate frequency they are emitted almost symmetrically with respect to the system axis because of momentum conservation. As a consequence, intensity correlations are observable in the far field when one considers symmetrical detection areas; more precisely, it has been possible to demonstrate analytically that almost complete noise reduction in the subtracted signals measured by two identical detectors can be achieved [2]. The theoretical model that we have developed includes both diffraction and linear dispersion of the signal field. However, all analytical results have been obtained within the perfectly monochromatic plane wave pump approximation. In order to obtain a more realistic description of the system we have also developed a numerical model which includes the effects of the finite size of the pump beam profile and its finite frequency bandwidth. It is important to investigate how these features affects the spatial quantum correlation phenomena predicted by the theory within the plane wave pump approximation, also in view to identify the better conditions under which these correlations can be observed in the experiment. Moreover, a stochatic method has been implemented in order to evaluate the intensity correlation function and the amount of intensity squeezing which can be achieved. [1] Quantum aspects of imaging, A.Gatti, E.Brambilla, L.A.Lugiato and M.Kolobov J. Opt. B, Quant. and Semiclass. Opt. 2, 196 (2000) [2] Quantum Entangled Images, A. Gatti, E. Brambilla, L.A. Lugiato and M.I. Kolobov, Phys. Rev. Lett. 83, 1763 (1999)
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