Observing photonic de Broglie waves without the NOON state

TL;DR

This study demonstrates that photonic de Broglie waves can be observed without photon number-path entanglement, showing that such waves are linked to measurement-induced indistinguishability rather than entanglement.

Contribution

It reveals that photonic de Broglie waves are observable without entanglement, challenging the previous notion that they are exclusive to NOON states.

Findings

Photonic de Broglie waves observed without entanglement.

Indistinguishable pathways, not entanglement, cause the wave phenomena.

Photonic de Broglie waves occur even with distinguishable photons.

Abstract

The photonic de Broglie wave, in which an ensemble of $N$ identical photons with wavelength $\lambda$ reveals $\lambda/N$ interference fringes, has been known to be a unique feature exhibited by the photon number-path entangled state or the NOON state. Here, we report the observation of the photonic de Broglie wave for a pair of photons, generated by spontaneous parametric down-conversion, that are not photon number-path entangled. We also show that the photonic de Broglie wave can even be observed for a pair of photons that are completely separable (i.e., no entanglement in all degrees of freedom) and distinguishable. The experimental and theoretical results suggest that the photonic de Broglie wave is, in fact, not related to the entanglement of the photons, rather it is related to the indistinguishable pathways established by the measurement scheme.