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Quantum Electronics and Laser Science Conference

Dispersion cancellation and non-classical noise reduction for large photon-number states

J. D. Franson, Michael J. Fitch

Published Jun 25, 2003• 0 citations
Publisher

Abstract

Summary form only given. Two classical pulses of light propagating through two distant, dispersive media will experience dispersion that depends only on the local properties of the two media. It was previously shown, however, that two entangled photons propagating through two dispersive media, can experience a cancellation of dispersion in the sense that the two photons will arrive at two equally-distant detectors at the same time despite the dispersion. Other forms of dispersion cancellation have also been described. We generalize dispersion cancellation to entangled states containing a large number N of photons in each pulse.

DOI
10.1109/qels.2002.1031027

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Summary form only given. Two classical pulses of light propagating through two distant, dispersive media will experience dispersion that depends only on the local properties of the two media. It was previously shown, however, that two entangled photons propagating through two dispersive media, can experience a cancellation of dispersion in the sense that the two photons will arrive at two equally-distant detectors at the same time despite the dispersion. Other forms of dispersion cancellation have also been described. We generalize dispersion cancellation to entangled states containing a large number N of photons in each pulse.
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.
Nonlocal dispersion cancellation is generalized to frequency-entangled states with large photon number N. We show that the same entangled states can simultaneously exhibit a factor of 1/N1/\sqrt{N}1/N​ reduction in noise below the classical shot noise limit in precise timing applications, as was previously suggested by Giovannetti, Lloyd, and Maccone [Nature (London) 412, 417 (2001)]. The quantum-mechanical noise reduction can be destroyed by a relatively small amount of uncompensated dispersion and entangled states of this kind have larger timing uncertainties than the corresponding classical states in that case. Similar results were obtained for correlated states, anticorrelated states, and frequency-entangled coherent states, which shows that these effects are a fundamental result of entanglement.
Two classical, coincident light pulses propagating through two different dispersive media will become broadened and their degree of coincidence will be reduced. The width of the coincidence curve can be shown to be proportional to ( β 1 2 + β 2 2 ) x 2 , where β1, and β2 are the dispersion coefficients in the two media and x is the distance traveled. When entangled photon pairs from parametric down conversion are considered instead, it is found that the width of the coincidence curve is then proportional to (β1 + β2)2x2, which gives an interference term of 2β1β1. If β1 = β2, the dispersion experienced by one photon can exactly cancel the dispersion experienced by the other in such a way that their coincidence is maintained.
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.
A pair of optical pulses traveling through two dispersive media will become broadened and, as a result, the degree of coincidence between the optical pulses will be reduced. For a pair of entangled photons, however, nonlocal dispersion cancellation in which the dispersion experienced by one photon cancels the dispersion experienced by the other photon is possible. In this paper, we report an experimental demonstration of nonlocal dispersion cancellation using entangled photons. The degree of two-photon coincidence is shown to increase beyond the limit attainable without entanglement. Our results have important applications in fiber-based quantum communication and quantum metrology.
When light propagates through complex media, its output spatial distribution is highly sensitive to its wavelength. This fundamentally limits the bandwidth of applications ranging from imaging to communication. Here, we demonstrate analytically and numerically that the spatial correlations of hyper-entangled photon pairs, simultaneously entangled spatially and spectrally, remain stable across a broad bandwidth: The chromatic modal dispersion experienced by one photon is canceled to first order by its spectrally anti-correlated twin, defining a "two-photon bandwidth" that can far exceed its classical counterpart. We illustrate this modal dispersion cancellation in multimode fibers, thin diffusers and blazed gratings, and demonstrate its utility for broadband wavefront shaping of quantum states. These findings advance our fundamental understanding of quantum light in complex media with applications in quantum imaging, communication, and sensing.