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arXiv:quant-ph/0012113 · Physical Review A

Continuously induced coherence without induced emission

Jaroslav Řeháček, Ladislav Mišta, Jaromı́r Fiurášek, Jan Peřina

Published Apr 4, 2002• 6 citations
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Abstract

Coherence properties of two down-converters continuously coupled via idler beams are analyzed. A formal equivalence between this device and two well-known experiments on quantum interference by Mandel's group is developed. As in these experiments the signal coherence is shown to be induced by a principal indistinguishability of signal photons. We also show that the which-way information about a signal photon carried by the idler beams periodically attains its maximum and minimum values in the course of the evolution. The optimal which-way measurement for our setup is constructed.

DOI
10.1103/physreva.65.043815

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Coherence properties of two down-converters continuously coupled via idler beams are analyzed. A formal equivalence between this device and two well-known experiments on quantum interference by Mandel's group is developed. As in these experiments the signal coherence is shown to be induced by a principal indistinguishability of signal photons. We also show that the which-way information about a signal photon carried by the idler beams periodically attains its maximum and minimum values in the course of the evolution. The optimal which-way measurement for our setup is constructed.
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.
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.
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.
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.