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Pure and Applied Optics Journal of the European Optical Society Part A

Anticoherence

L. Mandeļ

Published Sep 1, 1998• 5 citations
Publisher

Abstract

The concept of second-order anticoherence of two optical fields is defined via a cross-correlation function of the form . It is shown that the corresponding signal and idler fields produced in the process of parametric downconversion are mutually anticoherent, and it is pointed out that this anticoherence has already been observed experimentally, if somewhat indirectly.

DOI
10.1088/0963-9659/7/5/002

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The concept of second-order anticoherence of two optical fields is defined via a cross-correlation function of the form . It is shown that the corresponding signal and idler fields produced in the process of parametric downconversion are mutually anticoherent, and it is pointed out that this anticoherence has already been observed experimentally, if somewhat indirectly.
Although the signal and idler light beams produced in the process of spontaneous parametric down-conversion are mutually incoherent and exhibit no one-photon interference, interference effects should be observable after either the signal or the idler is reflected by a phase-conjugate mirror. The degree of coherence can, in principle, be as large as unity. We refer to the relationship between the signal and the idler produced by down-conversion as anticoherent and introduce a natural measure for the degree of anticoherence. \textcopyright{} 1996 The American Physical Society.
Normally, the signal and idler photons produced in the process of parametric down- conversion exhibit no second-order interference. However, in the presence of an external laser beam that follows the path of the signal photon and induces stimulated down-conversions, one would expect coherence to develop between the down-converted signal and idler beams. We have demonstrated the existence of this phenomenon in an experiment with two down-converters pumped by similar pump beams, in which two mutually coherent laser beams followed the paths of the two down-converted signal photons and induced coherence between the two down- converted idler beams. The induced coherence gives rise to observable interference effects, which are presented.
When a laser beam interacts with a nonlinear crystal, some of the incident photons fission into two lower frequency signal and idler photons through the process of spontaneous parametric downconversion. It is shown that, as a result of the strong positive correlation between signal and idler photons, the normalized intensity cross-correlation function λ12(τ) should be inversely proportional to the downconverted light intensity and ideally should be given by the inverse of the mean number of photons counted in the resolving time. This unusual relationship, which is a reflection of the quantum mechanical character of the downconverted optical field, has been confirmed in photoelectric counting measurements. The experiment makes use of the light from an argon-ion laser oscillating at 351.1 nm interacting with an 8-cm long crystal of KDP. The downconverted light is extracted at 633.5 and 788.0 nm in two directions that satisfy the phase-matching condition and is allowed to fall on two counting photomultipliers. The output pulses are fed to a time-to-digital converter that yields the cross-correlation function.
Parametric downconversion is a nonlinear optical process in which three fields are involved: pump, signal, and idler. The signal and idler separately may have fairly large uncertainty of frequencies and momenta, but if one frequency or momentum is measured, the other one is known with certainty because of the phase matching conditions whose physical meanings are momentum and energy conservations. In addition, the signal and idler pair was also shown to "remember" the phase of the pump photon.
In the Wigner formalism, after giving a general description of a light beam, the theory of parametric down-conversion is developed to second-order in the coupling constant. We then describe the detection process by calculating the auto-correlation and cross-correlations of the signal and idler beams. Four recent experiments are analyzed in detail: interference on a screen, Franson's experiments [Phys. Rev. Lett. 62, 2205 (1989)], Rarity and Tapster's experiments [Phys. Rev. Lett. 64, 2495 (1990)], and induced coherence without induced emission [X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991)].