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Physical Review A

Induced coherence without induced emission

L. J. Wang, X. Y. Zou, L. Mandeļ

Published Oct 1, 1991• 342 citations
Publisher

Abstract

An interference experiment with signal and idler photons produced by parametric down-conversion in two nonlinear crystals is described and analyzed theoretically. It is found that when the idlers for the two crystals are superposed and aligned, the idler photon from the first crystal can induce coherence between the two signals, but without inducing any additional emission. Blocking the first idler wipes out the interference. The implications for the interpretation of the quantum state vector are discussed, and this leads to the conclusion that the state reflects not only what is known, but to some extent also what is knowable in principle.

DOI
10.1103/physreva.44.4614

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An interference experiment with signal and idler photons produced by parametric down-conversion in two nonlinear crystals is described and analyzed theoretically. It is found that when the idlers for the two crystals are superposed and aligned, the idler photon from the first crystal can induce coherence between the two signals, but without inducing any additional emission. Blocking the first idler wipes out the interference. The implications for the interpretation of the quantum state vector are discussed, and this leads to the conclusion that the state reflects not only what is known, but to some extent also what is knowable in principle.
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.
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.
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.
The nonclassical phenomenon of ``induced coherence without simulated emission'' is analyzed under the condition where two nonlinear ${\mathrm{\ensuremath{\chi}}}^{(2)}$ crystals are aligned in such a way that their idler emissions are collinear and inside a ringlike cavity with loss. This forced indistinguishability of the idler photons produces an interference between the free traveling conjugated signal beams when they are superposed. This interference is independent of the cavity loss, within the limits of a single-mode theory, and highly dependent on the position of the crystals inside the cavity. The maximum obtainable visibility of 100% reflects an induced coherence in the two crystals by the cavity field.
Abstract Induced coherence in parametric down-conversion between two coherently pumped nonlinear crystals that share a common idler mode can be used as an imaging technique. Based on the interference between the two signal modes of the crystals, an image can be reconstructed. By obtaining an expression for the interference pattern that is valid in both the low- and the high-gain regimes of parametric down-conversion, we show how the coherence of the light emitted by the two crystals can be controlled. With our comprehensive analysis we provide deeper insight into recent discussions about the application of induced coherence to imaging in different regimes. Moreover, we propose a scheme for optimizing the visibility of the interference pattern so that it directly corresponds to the degree of coherence of the light generated in the two crystals. We find that this scheme leads in the high-gain regime to a visibility arbitrarily close to unity.