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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

“Nonlocal” dispersion cancellation with classical light

V. Torres-Company, Hanna Lajunen, Ari T. Friberg

Published Jun 1, 2009• 1 citation
Publisher

Abstract

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.

DOI
10.1109/cleoe-eqec.2009.5194772

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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.
Recently the engineering of the entanglement for photon pairs generated during the spontaneous parametric down conversion process (SPDC) can be achieved via manipulation of pump wavelength behind a \c{hi}(2)-based type II SPDC process [1]. Such effect is used in this paper for demonstration of non-classical dispersion cancellation phenomenon in both local and nonlocal detections, theoretically. The following results are analytically achieved: I) For local detection, if narrow pump laser (highly entangled photons) are used, the dispersive broadening cancelation is directly depends on the degree of entanglement. The higher entanglement degree, the more compensation occurs. The results indicate that by increasing the FWHM of the pump the impact of the entanglement degree is decreased in such a way that for a pump with FWHM=4 nm the entanglement has no effect on the broadening. Therefore, the dispersive broadening is only depends on the temporal walk-off between generated photon pairs and the pump. II) For nonlocal detection, it is also shown that entanglement cancels the dispersive broadening if and only if each of the generated paired photons propagate through dispersive material with identical length with opposite group velocity sign.
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.
It is a well-known and remarkable fact that in certain coincidence photon-counting experiments with cw-pumped parametric down-converters, the effects of group-velocity dispersion arising from media interposed between source and detectors are completely canceled, even if the media physically affect only one of the photons of the pair. Recently Perina et al. [Phys. Rev. A 59, 2359 (1999)] showed that this phenomenon does not occur when certain classical timing information is available about the arrival of individual photons at the detectors, as is the case when the photon pairs are produced via spontaneous parametric down-conversion using an ultrashort pump pulse. In this paper we show that the nonlocal cancellation of dispersion for such a source of entangled photons can be restored in principle by proper engineering of the source properties. In particular, we describe techniques for recovering interference in coincidence-counting experiments by suppressing distinguishing information without the post selection of photons. Moreover, a precise classical timing signal coincident with the photon pair is still available.
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.
Classically, two coincident light pulses propagating through two dispersive media will become broadened and their degree of coincidence will be reduced. When entangled photon pairs from parametric down-conversion are considered instead, it is found that the dispersion experienced by one photon can exactly cancel the dispersion experienced by the other in such a way that their coincidence is maintained. The dispersion cancellation is independent of the separation between the two photons and provides a further example of the nonlocal nature of the quantum theory.