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arXiv:1006.5854 · Physical Review A

Entanglement-based signature of nonlocal dispersion cancellation

Tomasz Wasak, Piotr Szańkowski, Wojciech Wasilewski, Konrad Banaszek

Published Nov 30, 2010• 31 citations
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Abstract

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.

DOI
10.1103/physreva.82.052120

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APS•Feb 1, 2010•0 citations
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.
Abstract We perform an experiment to verify the presence of entanglement in photon pairs. By sending down-converted light through dispersive media with opposite group velocity dispersion coefficients, we overcome the minimum broadening of temporal correlation for classical light. Entanglement is proved via an inequality derived directly from Heisenberg’s uncertainty principle. We present a criterion to select a suitable down-conversion source. Moreover, we introduce a new method to analyze the temporal correlations between the entangled photons.
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.
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.
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.
We present an investigation of the temporal correlation of time-energy entangled photon pairs propagating through multi-frequency-channel dispersive media, in which photon spectra spread over multiple discrete frequency channels with dispersions. We have observed more complex coincidence structures including double coincidence envelopes and dependence on frequency detuning that are absent in the single-channel case. Our results on the correlation of the time-energy photonic entanglement in dispersive media with channel divisions would impact the fields of quantum metrology and communication.
Franson’s paradigm for nonlocal dispersion cancellation [J. D. Franson, Phys. Rev. A 45, 3126 (1992)] is studied using two kinds of jointly Gaussian-state signal and reference beams with phase-sensitive cross correlations. The first joint signal-reference state is nonclassical, with a phase-sensitive cross correlation that is at the ultimate quantum-mechanical limit. It models the outputs obtained from continuous-wave spontaneous parametric down-conversion. The second joint signal-reference state is classical—it has a proper P representation—with a phase-sensitive cross correlation that is at the limit set by classical physics. Using these states we show that a version of Franson’s nonlocal dispersion cancellation configuration has essentially identical quantum and classical explanations except for the contrast obtained, which is much higher in the quantum case than it is in the classical case. This work bears on Franson’s recent article [J. D. Franson, Phys. Rev. A 80, 032119 (2009)], which asserts that there is no classical explanation for all the features seen in quantum nonlocal dispersion cancellation.