Testing Spatial Noncommutativity via Rydberg Atoms

Abstract

The possibility of testing spatial noncommutativity via Rydberg atoms is explored. An atomic dipole of a cold Rydberg atom is arranged in appropriate electric and magnetic field, so that the motion of the dipole is constrained to be planar and rotationally symmetric. Spatial noncommutativity leads to that the canonical angular momentum possesses fractional values. In the limit of vanishing kinetic energy, the dominate value of the lowest canonical angular momentum takes $\hslash /2$. Furthermore, in the limit of eliminating magnetic field, the dominate value of the lowest canonical angular momentum changes from $\hslash /2$ to $\hslash /4$. This result is a clear signal of spatial noncommutativity. An experimental verification of this prediction is suggested.

Comments: 10 pages. Physical Review Letters (in press)