  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, n, and critical atom
number, N, cannot be minimized simultaneously, so that an "optimal" sphere size
is taken to be the radius for which the geometric mean, (n x N)^(1/2), 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 (852nm) using fused-silica microspheres, for
which the maximum coupling coefficient g/(2*pi)=750MHz occurs for a sphere
radius a=3.63microns corresponding to the minimum for n=6.06x10^(-6). By
contrast, the minimum for N=9.00x10^(-6) occurs for a sphere radius of
a=8.12microns, while the optimal sphere size for which (n x N)^(1/2) is
minimized occurs at a=7.83microns. On an experimental front, we have fabricated
fused-silica microspheres with radii a=10microns and consistently observed
quality factors Q=0.8x10^(7). 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.
