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

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Submission date: 28. Aug. 2017
Pages: 8
published in: Physical review letters, 118 (2017), art-no. 180402 
DOI number (of the published article): 10.1103/PhysRevLett.118.180402
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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∕ 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.