Ultra-high-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 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, 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*pi) exceeding 700 MHz and critical atom numbers approaching 10^{-7} in optimized structures. Furthermore, preliminary experimental measurements of toroidal cavities at a wavelength of 852 nm indicate that quality factors in excess of 100 million can be obtained in a 50 micron principal diameter cavity, which would result in strong coupling values of (g/(2*pi),n_0,N_0)=(86 MHz,4.6*10^{-4},1.0*10^{-3}). 
S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut,   H. J. Kimble