de Broglie Waves

Georges Lochak

SU Zhao-xia

The paper expounds the background , content and experimental testing of De Broglie hypothesis,states the conception of De Broglie wave and its speed , corrects several wrong understanding on De Broglie wave and gives the right explanation;and so it has reference value for the teaching of De Broglie hypothesis and De Broglie Wave .

Iain G. Main

Daniel Shanahan

In his famous doctoral dissertation, de Broglie assumed that a massive particle is surrounded in its rest frame by a standing wave. He argued that as observed from another inertial frame this wave becomes the superluminal wave now known as the de Broglie wave. It is shown here that under a Lorentz transformation, such a standing wave becomes, not the de Broglie wave, but a modulated wave moving at the velocity of the particle. It is the modulation that has the superluminal velocity of the de Broglie wave and should be recognized as the true de Broglie wave. De Broglie's demonstrations relied, variously, on his "theorem of the harmony of phases", on a mechanical model, and on a spacetime diagram. It is shown that in each case the underlying wave was inadvertently suppressed. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, avoiding the awkward device of recovering the particle velocity from a superposition of such waves. The deeper wave structure implied by this de Broglie wave must also impinge on such issues in quantum mechanics as the meaning of the wave function and the nature of wave-particle duality.

J. R. Croca

Byoung Seung HAM

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.