Testing quantum duality using cold Rydberg atoms

Classically, the dynamics of the chiral oscillator (CO) may be described by the Landau model (LM) through a well established mathematical procedure known as duality mapping. In this letter we show how this duality is broken in quantum mechanics due to the presence of a $Z_2$-anomaly in the CO. We give the theoretical basis for an experimental setup displaying the possibility to measure this global anomaly using cold Rydberg atoms.