Ultrahigh-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>toroidal microresonators for cavity quantum electrodynamics

Abstract

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 $g∕2\ensuremath{\pi}$ exceeding $700\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and critical atom numbers approaching ${10}^{\ensuremath{-}7}$ in optimized structures. Furthermore, preliminary experimental measurements of toroidal cavities at a wavelength of $852\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ indicate that quality factors in excess of ${10}^{8}$ can be obtained in a $50\text{\penalty1000-\hskip0pt}\ensuremath{\mu}\mathrm{m}$ principal diameter cavity, which would result in strong-coupling values of $\mathbf{(}g∕(2\ensuremath{\pi}),{n}_{0},{N}_{0}\mathbf{)}=(86\phantom{\rule{0.3em}{0ex}}\mathrm{MHz},4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4},1.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3})$.