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Annual Meeting Optical Society of America

Is an empty de Broglie pilot wave capable of inducing coherence?

X. Y. Zou, T. Grayson, L. J. Wang, L. Mandeļ

Published Jan 1, 1992• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1992.muu3

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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.
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.
Photonic de Broglie waves (PBWs) via two-mode entangled photon pair interactions on a beam splitter show a pure quantum feature which cannot be obtained by classical means1-4. Although PBWs have been intensively studied for quantum metrology5-13 and quantum sensing14-25 over the last several decades, their implementation has been limited due to difficulties of high-order NOON state generation4. Recently a coherence version of PBWs, the so-called coherence de Broglie waves (CBWs), has been proposed in a pure classical regime of an asymmetrically coupled Mach-Zehnder interferometer (MZI)26. Unlike PBWs, the quantumness of CBWs originates from the cascaded quantum superposition of the coupled MZI. Here, the first CBWs observation is presented in a pure classical regime and discussed for its potential applications in coherence quantum metrology to overcome conventional PBWs limited by higher-order entangled photons. To understand the quantum superposition-based nonclassical features in CBWs, various violation tests are also performed, where asymmetrical phase coupling is the key parameter for CBWs.
Of all basic principles of classical physics, realism should arguably be the last to be given up when seeking a better interpretation of quantum mechanics. We examine the de Broglie-Bohm pilot wave theory as a well-developed example of a realistic theory. We present three challenges to a naive reading of pilot wave theory, each based on a system of several entangled particles. With the help of a coarse graining of pilot wave theory into a discrete system, we show how these challenges can be answered. However, this comes with a cost. In the description of individual systems, particles appear to scatter off empty branches of the wave function as if they were particles and conversely travel through particles as if they were waves. More generally, the ``particles'' of pilot wave theory are led by the guidance equation to move in ways no classical particle would, involving apparent violations of the principles of inertia and momentum conservation. We next argue that the aforementioned cost can be avoided within a retrocausal model. In the proposed version of the pilot wave theory, the particle is guided by a combination of advanced and retarded waves. The resulting account for quantum physics seems to have greater heuristic power, demands less damage to intuition, and moreover provides some general hints regarding spacetime and causality. This is the first of two papers. In the second [E. Cohen, M. Cort\^es, A. C. Elitzur, and L. Smolin, Realism and causality. II. Retrocausality in energetic causal sets, Phys. Rev. D 102, 124028 (2020).], we show that, in the context of an explicit model, retrocausality, with respect to an effective, emergent spacetime metric, can coexist with a strict irreversibility of causal processes.
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.
In quantum mechanics, photonic de Broglie waves have been understood as a unique property of quantum mechanics satisfying the complementarity between particle and wave natures of light, where the photonic de Broglie wavelength is inversely proportional to the number of entangled photons acting on a beam splitter. Very recently, the heart of nonclassical feature of photon bunching on a beam splitter was newly interpreted using pure wave nature of coherence optics [arXiv:1911.07174v2], paving a road to unconditionally secured classical key distribution [arXiv:1807.04233v3]. Here, Mach-Zehnder interferometer-based deterministic photonic de Broglie waves are studied in a coherence regime for both fundamental physics and potential applications of coherence-quantum metrology.