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

TL;DR

This study demonstrates that $|F,m=0>$ spin states in laser-cooled rubidium exhibit a topological and parity-dependent phase shift when the magnetic field is reversed adiabatically, confirmed through Ramsey interferometry.

Contribution

It experimentally verifies the topological and parity-dependent phase acquired by $m=0$ spin states during magnetic field reversal, a prediction previously unconfirmed.

Findings

Adiabatic magnetic field reversal induces a $ extbf{B} o - extbf{B}$ phase shift of $ extbf{ extpi}$.

No phase shift occurs during sudden reversal.

The phase factor depends on the parity of F, specifically $(-1)^F$.

Abstract

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 $\textbf{B} \to -\textbf{B}$.