Optimal sizes of dielectric microspheres for cavity QED with strong coupling

The whispering gallery modes ~WGMs! of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics ~cavity QED!. Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number n0 and critical atom number N0 cannot be minimized simultaneously, so that an ‘‘optimal’’ sphere size is taken to be the radius for which the geometric mean An0N0, is minimized. While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the D2 transition in atomic cesium at l05852 nm using fused-silica microspheres, for which the maximum coupling coefficient ga /(2p)'750 MHz occurs for a sphere radius a53.63 mm corresponding to the minimum for n0'6.06 310. By contrast, the minimum for N0'9.00310 26 occurs for a sphere radius of a58.12 mm, while the optimal sphere size for which An0N0 is minimized occurs at a57.83 mm. On an experimental front, we have fabricated fused-silica microspheres with radii a;10 mm and consistently observed quality factors Q>0.8 310. These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling.