A double-slit `which-way' experiment on the complementarity--uncertainty debate

TL;DR

This paper investigates the relationship between wave-particle complementarity and uncertainty in a double-slit experiment using weak measurement, revealing a complex momentum transfer distribution that challenges traditional views.

Contribution

It introduces a weak measurement approach to analyze momentum transfer in a double-slit experiment, providing new insights into the complementarity--uncertainty debate.

Findings

Distribution of momentum transfer extends beyond traditional bounds

Variance of momentum transfer is consistent with zero

Weak measurement reveals complex momentum transfer dynamics

Abstract

A which-way measurement in Young's double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenberg's uncertainty principle: distinguishing two positions a distance s apart transfers a random momentum q \sim \hbar/s to the particle. This claim has been subject to debate: Scully et al. asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al. asserted that Bohr's stance is always valid. We address this issue using the experimental technique of weak measurement. We measure a distribution for q that spreads well beyond [-\hbar/s, \hbar/s], but nevertheless has a variance consistent with zero. This weakvalued momentum-transfer distribution P_{wv}(q) thus reflects both sides of the debate.