Superradiant lifetime: Its definitions and relation to absorption length

Abstract

The literature contains three definitions of superradiant lifetime, standing in the ratio 1:2:4. The first may be defined by ${\tau }^{\mathrm{RE}}=\frac{T_1}{N\mu }$, where $\mu$ is the geometrical factor of Rehler and Eberly. The second appears naturally in Dicke's equation $\dot{\phi }={\left({\tau }^{\mathrm{D}}\right)}^{-1\mathrm{}}sin\phi$. The third may be defined, following Arecchi and Courtens, by $I=\frac{\hslash {\omega }_0}{{\tau }^{\mathrm{AC}}}$ for a maximally superradiant sample. For large Fresnel number, $\mu =\left(\frac{3}{8\pi }\right)\frac{{\lambda }^2}{A}$; the numerical coefficient has been calculated incorrectly by some authors, so that the resulting formulas for superradiant lifetime do not match the definitions. The many superradiant lifetimes in current use are identified with the above three.