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 √n₀N₀, 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 λ₀=852nm using fused-silica microspheres, for which the maximum coupling coefficient g_a/(2π)≈750MHz occurs for a sphere radius a=3.63μm corresponding to the minimum for n₀≈6.06×10^-6. By contrast, the minimum for N₀≈9.00×10^-6 occurs for a sphere radius of a=8.12μm, while the optimal sphere size for which √n₀N₀ is minimized occurs at a=7.83μm. On an experimental front, we have fabricated fused-silica microspheres with radii a∼10μm and consistently observed quality factors Q>~0.8×10⁷. 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.