  This thesis describes a study of a cavity QED microlaser in which many atoms
are present simultaneously and atom-cavity interaction is well-defined. The
microlaser is found to display multiple thresholds analogous to first-order
phase transitions of the cavity field. Hysteresis is observed as a function of
atom-cavity detuning and number of atoms. Data is compared with a rate equation
model and fully quantized treatment based on micromaser theory. Good agreement
between theory and experiment is found when the cavity is resonant with atoms
of the most probable velocity, but long lifetimes of metastable states preclude
the observation of true steady-state transition points. For nonzero atom-cavity
detuning the microlaser displays broadenings and shifts which are not yet
well-understood. Quantum trajectory simulations are performed to investigate
many-atom and finite transit time effects in the microlaser. We show that over
a wide range of parameters the many-atom microlaser scales with the single-atom
theory, with a perturbation in the photon statistics due to cavity decay during
the atom transit time.
