Vanishing electric dipole transition moment

Abstract

We have discovered an interference which results in the vanishing of some electric dipole transition amplitudes. A transition-matrix element $T$ between certain $S$ and $P$ sublevels with the same value of ${M}_{F}$ vanishes when an applied magnetic field satisfies ${X}_{s}+{X}_{p}=\ensuremath{-}2{M}_{F}$, where $X={\ensuremath{\mu}}_{B}{g}_{J}\frac{B}{A}$, and $A$ is the hfs constant. There must be an avoided crossing between the two states of the same ${M}_{F}$ which can only occur when one of the hyperfine manifolds has an inverted Zeeman effect. These conditions imply ${M}_{F}<0$ and $I>J$. We observed the vanishing of $T$ in $^{23}\mathrm{Na}$ for one of the $\ensuremath{\Delta}{M}_{F}=0$ optical transitions of the $3{S}_{\frac{1}{2}}(F=1)\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}(F=1)$ manifold. Absorption of cw laser light was monitored by observing total fluorescence perpendicular to both the atomic and laser beams, and absorption vanished near an applied field of 155 G. $T$ vanishes for a large number of cases including rf and microwave frequencies and is a rather general consequence of angular momentum selection rules and perturbation theory. This phenomenon may have application in optical pumping, Lamb-shift measurements, and atomic weak neutral-current experiments.