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Journal of Modern Optics

Study of Induced Temporal Coherence in Optical Parametric Down Conversion

Alexander V. Sergienko, Yanhua H. Shih, Morton H. Rubin

Published Aug 1, 1993• 4 citations
Publisher

Abstract

Temporal coherence of the idler photon beam induced by a coherent input signal was studied for non-degenerate optical parametric down conversion. When the optical path difference of the interferometer is much longer than the coherence length of the spontaneous idler radiation, the experimental results show that the first-order temporal coherence of the idler photon can be induced by a coherence input signal and the interference fringe visibility is determined by the intensity of the coherent input signal.

DOI
10.1080/09500349314551481

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Temporal coherence of the idler photon beam induced by a coherent input signal was studied for non-degenerate optical parametric down conversion. When the optical path difference of the interferometer is much longer than the coherence length of the spontaneous idler radiation, the experimental results show that the first-order temporal coherence of the idler photon can be induced by a coherence input signal and the interference fringe visibility is determined by the intensity of the coherent input signal.
We perform a time-resolved quantum interference experiment based on the effect of induced coherence without induced emission using two pulsed parametric down-conversion sources. We periodically vary the transmission of the first source's idler beam and measure the time-dependent visibility of fringes in the interference between the two signal beams. The visibility is found to be correlated with the transmissivity with a time delay corresponding to a combined path of the first idler and the second signal beam. The experiment is discussed in the context of the delayed choice experiments.
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.
We show that temporal two-photon interference effects involving the signal and idler photons created by parametric down-conversion can be fully characterized in terms of the variations of two length parameters---called the biphoton path-length difference and the biphoton path-asymmetry-length difference---which we construct using the six different length parameters that a general two-photon interference experiment involves. We perform an experiment in which the effects of the variations of these two parameters can be independently controlled and studied. In our experimental setup, which does not involve mixing of signal and idler photons at a beam splitter, we further report observations of Hong-Ou-Mandel- (HOM-)like effects both in coincidence and in one-photon count rates. As an important consequence, we argue that the HOM and the HOM-like effects are best described as observations of how two-photon coherence changes as a function of the biphoton path-asymmetry-length difference.
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.
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.
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.