Characterization of non-classical particle propagation using superpositions of position and momentum

TL;DR

This paper experimentally investigates how superpositions of position and momentum states in photons reveal interference effects that challenge classical notions of particle propagation, demonstrating quantum localization and negativity of the Wigner function.

Contribution

It provides a detailed experimental analysis of photon propagation in superpositions of position and momentum, highlighting interference effects and quantum localization phenomena.

Findings

Interference localizes photons in narrow position and momentum intervals.

Violation of Newton's first law observed at intermediate propagation times.

Negativity of the Wigner function demonstrated outside initial uncertainty regions.

Abstract

The uncertainty principle suggests a quantitative trade-off between the control of position and the control of momentum in particle propagation. However, a superposition of two states with very different uncertainty trade-offs introduces an interference term that seems to combine precise statements about position and about momentum, allowing us to study how quantum mechanics describes the propagation of individual particles in free space. Here, we present a detailed experimental study of photons prepared in a superposition of position and momentum generated in a Sagnac interferometer. The transverse distribution of photons was obtained with three different measurement settings at the output port of the interferometer, corresponding to the initial position distribution, the initial momentum distribution, and an intermediate propagation time at which the contributions of initial position and momentum uncertainties are approximately equal to each other. We show that the interference effect localizes the photons in narrow intervals of position and momentum, resulting in a quantitative violation of Newton's first law as the interference pattern spreads out at the intermediate position. The data obtained can be used to demonstrate the negativity of the Wigner function in regions outside the position and momentum intervals in which the position and momentum contributions are confined.