A common experimental setup in cavity quantum electrodynamics (QED) consists
of a single two-level atom interacting with a single mode of the
electromagnetic field inside an optical cavity. The cavity is externally driven
and the output is continuously monitored via homodyne measurements. We derive
formulas for the optimal rates at which these measurements provide information
about (i) the quantum state of the system composed of atom and electromagnetic
field, and (ii) the coupling strength between atom and field. We find that the
two information rates are anticorrelated.Comment: 11 pages, 1 figure, final versio