Ultrahigh- Q toroidal microresonators for cavity quantum electrodynamics

We investigate the suitability of toroidal microcavities for strong-coupling cavity quantum electrodynamics (QED). Numerical modeling of the optical modes demonstrate a significant reduction of the modal volume with respect to the whispering gallery modes of dielectric spheres, while retaining the high-quality factors representative of spherical cavities. The extra degree of freedom of toroid microcavities can be used to achieve improved cavity QED characteristics. Numerical results for atom-cavity coupling strength $g$, critical atom number ${N}_{0}$, and critical photon number ${n}_{0}$ for cesium are calculated and shown to exceed values currently possible using Fabry-Perot cavities. Modeling predicts coupling rates $g∕2ensuremath{pi}$ exceeding $700phantom{rule{0.3em}{0ex}}mathrm{MHz}$ and critical atom numbers approaching ${10}^{ensuremath{-}7}$ in optimized structures. Furthermore, preliminary experimental measurements of toroidal cavities at a wavelength of $852phantom{rule{0.3em}{0ex}}mathrm{nm}$ indicate that quality factors in excess of ${10}^{8}$ can be obtained in a $50text{penalty1000-hskip0pt}ensuremath{mu}mathrm{m}$ principal diameter cavity, which would result in strong-coupling values of $mathbf{(}g∕(2ensuremath{pi}),{n}_{0},{N}_{0}mathbf{)}=(86phantom{rule{0.3em}{0ex}}mathrm{MHz},4.6ifmmodetimeselsetexttimesfi{}{10}^{ensuremath{-}4},1.0ifmmodetimeselsetexttimesfi{}{10}^{ensuremath{-}3})$.