Scheme for directly observing the non-commutativity of the position and the momentum operators with interference

TL;DR

This paper proposes an experimental scheme using single-photon interference to directly observe the non-commutativity of position and momentum operators, providing a new way to test fundamental quantum relations.

Contribution

It introduces a novel experimental method for directly demonstrating the non-commutativity of position and momentum operators through quantum interference.

Findings

The scheme enables direct observation of position-momentum non-commutativity.

Analysis applies to both photonic and matter-wave interference.

Potential for testing quantum mechanics with massive particles.

Abstract

Although non-commutativity of a certain set of quantum operators (e.g., creation/annihilation operators and Pauli spin operators) has been shown experimentally in recent years, the commu- tation relation for the position and the momentum operators has not been directly demonstrated to date. In this paper, we propose and analyze an experimental scheme for directly observing the non-commutativity of the position and the momentum operators using single-photon quantum in- terference. While the scheme is studied for the single-photon state as the input quantum state, the analysis applies equally to matter-wave interference, allowing a direct test of the position-momentum commutation relation with a massive particle.