  We report the use of broadband heterodyne spectroscopy to perform continuous
measurement of the interaction energy between one atom and a high-finesse
optical cavity, during individual transit events of $\sim 250$ $\mu$s duration.
Measurements over a wide range of atom-cavity detunings reveal the transition
from resonant to dispersive coupling, via the transfer of atom-induced signals
from the amplitude to the phase of light transmitted through the cavity. By
suppressing all sources of excess technical noise, we approach a measurement
regime in which the broadband photocurrent may be interpreted as a classical
record of conditional quantum evolution in the sense of recently developed
quantum trajectory theories.
