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Physical Review Letters

Induced coherence and indistinguishability in optical interference

X. Y. Zou, L. J. Wang, L. Mandeļ

Published Jul 15, 1991• 641 citations
Publisher

Abstract

Second-order interference is observed in the superposition of signal photons from two coherently pumped parametric down-converters, when the paths of the idler photons are aligned. The interference exhibits certain nonclassical features; it disappears when the idlers are misaligned or separated by a beam stop. The interpretation of this effect is discussed in terms of the intrinsic indistinguishability of the photon paths.

DOI
10.1103/physrevlett.67.318

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Second-order interference is observed in the superposition of signal photons from two coherently pumped parametric down-converters, when the paths of the idler photons are aligned. The interference exhibits certain nonclassical features; it disappears when the idlers are misaligned or separated by a beam stop. The interpretation of this effect is discussed in terms of the intrinsic indistinguishability of the photon paths.
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.