Testing Spatial Noncommutativity via Magnetic Hyperfine Structure Induced by Fractional Angular Momentum of Rydberg System

An approach to solve the critical problem of testing quantum effects of spatial noncommutativity is proposed. Magnetic hyperfine structures in a Rydberg system induced by fractional angular momentum originated from spatial noncommutativity are discussed. The orders of the corresponding magnetic hyperfine splitting of spectrum $\sim 10^{-7} - 10^{-8} eV$ lie within the limits of accuracy of current experimental measurements. Experimental tests of physics beyond the standard model are the focus of broad interest. We note that the present approach is reasonable achievable with current technology. The proof is based on very general arguments involving only the deformed Heisenberg-Weyl algebra and the fundamental property of angular momentum. Its experimental verification would constitute an advance in understanding of fundamental significance, and would be a key step towards a decisive test of spatial noncommutativity.