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Physical Review Letters

Can an ‘‘empty’’ de Broglie pilot wave induce coherence?

X. Y. Zou, Timothy P. Grayson, L. J. Wang, L. Mandeļ

Published Jun 22, 1992• 30 citations
Publisher

Abstract

According to the de Broglie pilot wave theory, a pilot wave which is empty of photons is still capable of physical effects like induced coherence. We have carried out an experiment to test this prediction. The experiment involves interference of photons produced by down-conversion in two nonlinear crystals and depends on the mutual coherence induced between the two signal beams by an idler. When the photon is removed from the idler by a beam splitter, it is found that the resulting ``empty pilot wave'' no longer induces coherence. This violates at least the Selleri-Croca version of the de Broglie pilot wave theory makes the physical reality of the corresponding pilot wave doubtful.

DOI
10.1103/physrevlett.68.3667

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According to the de Broglie pilot wave theory, a pilot wave which is empty of photons is still capable of physical effects like induced coherence. We have carried out an experiment to test this prediction. The experiment involves interference of photons produced by down-conversion in two nonlinear crystals and depends on the mutual coherence induced between the two signal beams by an idler. When the photon is removed from the idler by a beam splitter, it is found that the resulting ``empty pilot wave'' no longer induces coherence. This violates at least the Selleri-Croca version of the de Broglie pilot wave theory makes the physical reality of the corresponding pilot wave doubtful.
The de Broglie pilot wave theory is a hybrid of quantum and classical concepts that was introduced in order to avoid the conceptual difficulties of the Copenhagen interpretation. According to some versions of this theory, there exist both photons and electromagnetic waves, and the waves are supposed not only to yield probabilities for the photons, but also to have a physical reality. Even an ″empty″ wave, which cannot give rise to photoelectric detection, is supposed to be capable of inducing observable effects. We have tested this theory in an experiment with two cascaded parametric down-converter crystals, in which the idler beam from the first crystal has been shown to induce coherence between the signal beams from the two crystals without inducing any emission. When the photon is removed from the first idler with the help of a beam splitter, the remaining empty wave is found not to induce coherence.
In this paper we discuss a recent double-slit experiment where which-path information is obtained without disturbing the photons in their path to the detector, and, as a consequence, an interference pattern is observed on the far screen even if it is known which slit the photons go through. We argue that this result is in clear contradiction with a fundamental principle in orthodox quantum mechanics – Bohr’s complementarity principle – and also point out that, on the other hand, the results of this experiment are the expected ones in the framework of de Broglie’s pilot wave theory
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.
An interferometric arrangement utilizing a pair of twin photons, generated by parametric down-conversion, is devised to show second-order interferences revealing de Broglie's wavelength of the photon pair as a whole and the Pancharatnam phase depending on the number of photons. This proposed experiment utilizes the phenomenon ``induced coherence without stimulated emission'' to generate a coherent superposition of states distinct from the usual superposition with beam splitters, where the photons are independently scattered. In this experiment interference occurs due to recombination of photon trajectories on a beam splitter and also through frustration or enhancement of the down-conversion processes.