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New Journal of Physics

‘Nonlocal’ dispersion cancelation with classical light

Hanna Lajunen, Ari T. Friberg

Published Jun 22, 2009• 26 citations
Publisher

Abstract

We show a classical analog of the original nonlocal dispersion cancelation effect in intensity interferometry with stationary light obeying Gaussian statistics. The dispersion compensation is due to the uncorrelation of the spectral components of the radiation. Although this classical counterpart phenomenon is not nonlocal in a strict quantum mechanical sense, it suggests that some second-order interference devices relying on temporal entanglement do not require a quantum light source.

DOI
10.1088/1367-2630/11/6/063041

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We show a classical analog of the original nonlocal dispersion cancelation effect in intensity interferometry with stationary light obeying Gaussian statistics. The dispersion compensation is due to the uncorrelation of the spectral components of the radiation. Although this classical counterpart phenomenon is not nonlocal in a strict quantum mechanical sense, it suggests that some second-order interference devices relying on temporal entanglement do not require a quantum light source.
In this work, we consider nonlocal dispersion cancellation with classical light in a setup. We demonstrate that the dispersion cancellation phenomenon of temporally entangled two-photon states of light in continuous-wave (CW) pumped SPDC can be similarly obtained in intensity interferometry with classical, stationary radiation that obeys Gaussian statistics. Specifically, we show that the correlation of the intensity fluctuations that would be measured in a setup plays the role of the temporally resolved intensity coincidence detection measured (a) (the original setup for the dispersion cancellation). The only difference is a different dispersion compensation rules which comes from the fact that CW-pumped SPDC photons are anticorrelated in frequency, whereas stationary light has, by definition, uncorrelated spectrum.
Shapiro recently argued that nonlocal dispersion cancellation using entangled pairs of photons is essentially classical in nature, based on a comparison with a classical model in which two stationary, chaotic beams of light have phases and frequencies that are anticorrelated, which he refers to as ``phase-sensitive'' light [J. H. Shapiro, Phys. Rev. A 81, 023824 (2010)]. It is shown here that there is no physical cancellation of dispersion for classical light of that kind and Shapiro's results merely reflect the fact that identical dispersion occurs in both beams. The origin of the cross correlations between the intensities of the two beams is shown to be completely different in the classical and quantum mechanical cases.
Several recent papers have shown that some forms of dispersion cancellation have classical analogs and that some aspects of nonlocal two-photon interferometry are consistent with local realistic models. It is noted here that the classical analogs only apply to local dispersion cancellation experiments [A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 68, 2421 (1992)] and that nonlocal dispersion cancellation [J. D. Franson, Phys. Rev. A 45, 3126 (1992)] is inconsistent with any classical field theory and has no classical analog. The local models that have been suggested for two-photon interferometry are shown to be local but not realistic if the spatial extent of the interferometers is taken into account. It is the inability of classical models to describe all of the relevant aspects of these experiments that distinguishes between quantum and classical physics, which is also the case in Bell's inequality.
We derive an inequality bounding the strength of temporal correlations for a pair of light beams prepared in a separable state and propagating through dispersive media with opposite signs of group-velocity dispersion. The presented inequality can be violated by entangled states of light, such as photon pairs produced in spontaneous parametric down-conversion. Because the class of separable states covers the entire category of classical fields as a particular case, this result provides an unambiguously quantum feature of nonlocal dispersion cancellation that cannot be reproduced within the classical theory of electromagnetic radiation.
We report the first experimental demonstration of even-order aberration cancellation in quantum interferometry. The effect is a spatial counterpart of the spectral group velocity dispersion cancellation, which is associated with spectral entanglement. It is manifested in temporal interferometry by virtue of the multiparameter spatial-spectral entanglement. Spatially entangled photons, generated by spontaneous parametric down-conversion, were subjected to spatial aberrations introduced by a deformable mirror that modulates the wave front. We show that only odd-order spatial aberrations affect the quality of quantum interference.