Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum

TL;DR

This paper derives and experimentally verifies new uncertainty relations for the three components of angular momentum in a spin-1/2 system, revealing a universal triple constant similar to that in position-momentum uncertainty.

Contribution

It introduces novel uncertainty relations involving all three angular momentum components and confirms the triple constant experimentally in a diamond spin system.

Findings

The triple constant 2/√3 appears in angular momentum uncertainty relations.

Experimental results confirm the theoretical triple constant.

The relations hold across a wide range of parameters.

Abstract

The uncertainty principle is considered to be one of the most striking features in quantum mechanics. In the textbook literature, uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of measurement outcomes for a pair of non-commuting observables. In this work, we study the preparation uncertainty for the angular momentum, especially in the spin-1/2 representation. We derive uncertainty relations encompassing the triple components of angular momentum, and show that compared with the relations involving only two components, a triple constant $2/\sqrt{3}$ often arises. Intriguingly, this constant is the same for the position and momentum case. Experimental verification is carried out on a single spin in diamond, and the results confirm the triple constant in a wide range of experimental parameters.