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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Influence of walk-off, dispersion, and diffraction on the coherence of parametric fluorescence

Antonio Picozzi, Marc Haelterman

Published Apr 18, 2001• 24 citations
Publisher

Abstract

We consider the basic problem of spontaneous parametric generation from quantum noise fluctuations in the presence of a continuous plane-wave pump. We show, both numerically and analytically, that the walk-off between the down-converted fields is the key ingredient that leads to the generation of coherent fields in the parametric process. Along these lines, our theory reveals that, in the absence of walk-off, diffraction and chromatic dispersion in usual quadratically nonlinear materials only lead to incoherent erratic dynamics. Moreover, a two-dimensional study shows that, when the walk-off is exclusively temporal (or spatial), the parametric process is not able to yield the generation of spatially (or temporally) coherent fields. This study sheds light on the problem of coherence in parametric fluorescence and, in particular, allows us to explain various recent experimental observations.

DOI
10.1103/physreve.63.056611

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We consider the basic problem of spontaneous parametric generation from quantum noise fluctuations in the presence of a continuous plane-wave pump. We show, both numerically and analytically, that the walk-off between the down-converted fields is the key ingredient that leads to the generation of coherent fields in the parametric process. Along these lines, our theory reveals that, in the absence of walk-off, diffraction and chromatic dispersion in usual quadratically nonlinear materials only lead to incoherent erratic dynamics. Moreover, a two-dimensional study shows that, when the walk-off is exclusively temporal (or spatial), the parametric process is not able to yield the generation of spatially (or temporally) coherent fields. This study sheds light on the problem of coherence in parametric fluorescence and, in particular, allows us to explain various recent experimental observations.
We examine experimentally how the degree of position-momentum entanglement of photon pairs depends on the transverse coherence of the pump beam that excites them in a process of spontaneous parametric down-conversion. Using spatially incoherent light from a light-emitting diode, we obtain strong position correlation of the photons, but we find that transverse momentum correlation, and thus entanglement, is entirely absent. When we continuously vary the degree of spatial coherence on the pump beam, we observe the emergence of stronger momentum correlations and entanglement. We present theoretical arguments that explain our experimental results. Our results shed light on entanglement generation and can be applied to control entanglement for quantum information applications.
We study the influence of group-velocity dispersion (or diffraction) on the coherence properties of the parametric three-wave interaction driven from an incoherent pump wave. We show that, under certain conditions, the incoherent pump may efficiently amplify a signal wave with a high degree of coherence, in contrast with the usual kinetic description of the incoherent three-wave interaction. The group-velocity dispersion is shown to be responsible for a spectral filtering process, in which the coherence of the generated signal increases, as the coherence of the pump wave decreases. As a result, the coherence acquired by the signal in the presence of an incoherent pump, is higher than that acquired in the presence of a fully coherent pump. The mechanism underlying this intriguing result is based on the emergence of a mutual coherence between the incoherent pump and the generated idler wave. We calculate explicitly the degree of mutual coherence between the pump and idler waves and show that the two incoherent waves become completely correlated in the full incoherent regime of interaction. The theory is in quantitative agreement with the numerical simulations. To motivate the experimental confirmation of our theory, we characterize the dispersion properties of an actual quadratic nonlinear optical crystal in which the process of signal coherence enhancement induced by pump incoherence may be studied experimentally.
We investigate the emergence of spatial and temporal coherence for the fields in the noncritical nondegenerate parametric second-order down-conversion process pumped with low spatial and temporal coherence beams. It is shown that in this scenario, which is of considerable practical importance, the parametric gain in the near field breaks down into an ensemble of mutually incoherent beamlets containing parametric waves. The field generated in a single beamlet is fully spatially coherent. The size of such coherent parametric gain regions is governed by the near-field spatial coherence radius of the pump, which also acts as a parameter, restraining the linear diffraction of the parametric waves generated in the nonlinear interaction. Furthermore, we experimentally demonstrate how the spatial and temporal coherence can be substantially enhanced by manipulating the spatial field correlation of the multilongitudinal and multi-transversal mode pump.
Ideal quantum frequency conversion (QFC) devices enable wavelength translation of a quantum state of light while preserving its essential quantum characteristics, namely photon statistics and coherence. However, the generation of noise photons due to spontaneous scattering of the strong classical pump used in the three-wave mixing process can limit QFC fidelity. We experimentally and theoretically characterize the noise properties of a difference-frequency generation device for QFC and find that fabrication errors in the quasi-phase-matching grating enhance generation of noise photons by parametric fluorescence.