Experimental Demonstration of Commutation Relations Using Intensity Correlations

TL;DR

This paper experimentally verifies the fundamental bosonic commutation relation for optical fields by measuring intensity correlations, confirming quantum theory predictions for both single-photon and coherent states.

Contribution

It provides the first direct experimental demonstration of the bosonic commutation relation using intensity correlation measurements.

Findings

Measured commutator expectation values are consistent with unity.

Results agree quantitatively with quantum theory.

Demonstrates a new method for testing quantum commutation relations.

Abstract

The canonical commutation relation is a cornerstone of quantum theory and underlies the Heisenberg uncertainty principle. Although uncertainty relations have been extensively tested, direct verifications of the underlying commutation relation itself have remained elusive. We report an experimental demonstration of the bosonic commutation relation for optical field operators based on measurements of two distinct intensity correlation functions. From these measurements, we extract the expectation value of the field-operator commutator for both a single-photon state and coherent state. In both cases, the measured values are consistent with unity, in quantitative agreement with quantum theory.