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Journal of the Optical Society of America B

Observation of induced coherence in two-photon downconversion

L. J. Wang, X. Y. Zou, L. Mandeļ

Published May 1, 1991• 44 citations
Publisher

Abstract

By using two mutually coherent light beams of adjustable intensity to induce downconversions of the signal beams in two similar nonlinear crystals and then allowing the two idlers to interfere, we measure the variation of the induced degree of coherence as a function of inducing intensity. The key parameter N is the average photon occupation number per mode of the inducing field. We show experimentally that the induced degree of coherence is given by N/(N+1), as is expected theoretically.

DOI
10.1364/josab.8.000978

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By using two mutually coherent light beams of adjustable intensity to induce downconversions of the signal beams in two similar nonlinear crystals and then allowing the two idlers to interfere, we measure the variation of the induced degree of coherence as a function of inducing intensity. The key parameter N is the average photon occupation number per mode of the inducing field. We show experimentally that the induced degree of coherence is given by N/(N+1), as is expected theoretically.
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.
Although induced coherence is generally associated with induced or stimulated emission, in the process of spontaneous parametric downconversion of light induced coherence can be generated on its own. This is demonstrated in an experiment in which the signal beams from two coherently pumped downconverters come together and interfere whenever the idler beam from the first downconverter (DC1) passes through and is aligned with the second downconverter (DC2). Misaligning the idlers, or blocking the first idler, makes the interference disappear. More generally, the degree of coherence can be controlled by varying the amplitude of the idler from DC1 that reaches DC2. The interpretation of this nonclassical interference is discussed in terms of the interpretation of the wave function or state vector of the emitted photon.
Induced coherence without induced emission has been obtained, in Mandel's group, through the alignment of the idler beams produced by two nonlinear crystals in parametric downconversion processes. The interference resulting between the two spontaneous signal beams emitted by the crystals is explained by the relationship between degree of coherence and degree of indistinguishability. Although the quantitative understanding of this interference has yet to be understood, the degree of visibility obtained from those interference patterns reflects the phase correlation established between the signal emission of the two crystals in the spontaneous downconversion process. Those experiments have explored this nonclassical phenomenon by inserting absorbers in the idler connection path between the two crystals, by insertion of optical delays, and even by a topological modification of the connection path by Pancharatnam's or Berry's phase in the optical domain. In all the experiments performed to date, the variations introduced in the connection path deliberately decreased the degree of indistinguishability and, consequently, the degree of coherence.
We discuss the situation in which idler beams from two parametric down-converter crystals are allowed to interfere. We show that, when two mutually coherent signal beams derived from a common laser are injected into the down-converters, the two idler beams can become mutually coherent also. Moreover, the resulting interference pattern can, in principle, have 100% visibility when the number of injected photons per unit down-converter bandwidth is large. This is just the condition for stimulated down-conversion to dominate over spontaneous down-conversion.
Measurements have been made of the rate at which signal photons are produced in a nonlinear crystal in the process of parametric downconversion, when a coherent light beam from a He:Ne laser is injected into the crystal in the direction of the conjugate-idler photons. The latter provides a stimulating field for the downconversion. When the phase matching condition inside the nonlinear medium is satisfied, the rate of downconversion is enhanced by the presence of the He–Ne laser beam by a factor of the form 1 + βIi, where li is the intensity of the He:Ne laser beam. The effect of defocusing either the pump beam or the He–Ne idler beam is investigated. Possible use of this phenomenon to study the photon amplifier with single-photon input will be discussed.
Coherence can be induced or stimulated in parametric down-conversion using two or three crystals when, for example, the idler modes of the crystals are aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114, 053601 (2015)] focused on which-path information and the role of vacuum fields in realizing complementarity via reduced visibility in single-photon interference. Here we describe experiments comparing induced and stimulated coherence. Different single-photon interference experiments were performed by blocking one of the pump beams in a three-crystal setup. Each counted photon is emitted from one of two crystals and which-way information may or not be available, depending on the setup. Distinctly different results are obtained in the induced and stimulated cases, especially when a variable transmission filter is inserted between the crystals. A simplified theoretical model accounts for all the experimental results and is also used to address the question of whether the phases of the signal and idler fields in parametric down-conversion are correlated.