We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
60/2017
Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum
Wenchao Ma, Bin Chen, Ying Liu, Mengqi Wang, Xiangyu Ye, Fei Kong, Fazhan Shi, Shao-Ming Fei and Jiangfeng Du
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 for spin-$1/2$. 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 $2/\sqrt3$ 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.
