The $E1$ & $M1$ Spontaneous Decay Rates for an Emitter Inside a Cavity Within a Medium

Abstract

We discuss the $E1$ and $M1$ spontaneous decay rates of the an emitter residing inside of a real cavity carved out of a vast, uniform, homogenous, isotropic, linear, lossless, dispersionless, and continuous medium. The ratio of the medium rate to vacuum rate is given by ${\Gamma }_m/{\Gamma }_0=[G(u){]}^2{n}^3/u$, where $G(u)=3u/(2u+1)$ is the local field correction factor, $n=\sqrt{\epsilon \mu /({\epsilon }_0{\mu }_0)}$ is the index of refraction of the medium, $\epsilon ({\epsilon }_0)$ is the electric permitivity of the medium (vacuum), $\mu ({\mu }_0)$ is the magnetic permeability of the medium (vacuum), and $u=\epsilon /{\epsilon }_0$ for $E1$ transitions or $u={\mu }_0/\mu$ for $M1$ transitions.

16 pages, no figures. This short note is based on an early draft of a paper we wrote describing our measurement of the hyperfine quenching rate of the clock transition in Yb-171, see http://dx.doi.org/10.1103/PhysRevLett.113.033003