Observation of Topological and Parity-dependent Phase of m=0 Spin States

A Ramsey interrogation scheme was used to measure the phase shift of laser-cooled $^{87}$Rb clock-transition pseudospins arising as a result of a reversal of a bias magnetic field, i.e., $\textbf{B} \to -\textbf{B}$, during the interrogation. While no phase shift occurred when the reversal was sudden, the Ramsey fringes were shifted by a factor of $\pi$ when the reversal was adiabatic. We thus verified the prediction that the spin states $|F,m=0 >$ acquire a purely topological and parity-dependent phase factor of $(-1)^{F}$ as a result of $\textbf{B} \to -\textbf{B}$.