A nonlinear spectroscopic investigation of a strongly coupled atom-cavity system is presented. A two-field pump-probe experiment is employed to study nonlinear structure as the average number of intracavity atoms is varied from N̅≈4.2 to N̅≈0.8. Nonlinear effects are observed for as few as 0.1 intracavity pump photons. A detailed semiclassical simulation of the atomic beam experiment gives reasonable agreement with the data for N̅≳2 atoms. The simulation procedure accounts for fluctuations in atom-field coupling which have important effects on both the linear and nonlinear probe transmission spectra. A discrepancy between the simulations and the experiments is observed for small numbers of atoms (N̅≲1). Unfortunately, it is difficult to determine if this discrepancy is a definitive consequence of the quantum nature of the atom-cavity coupling or a result of the severe technical complications of the experiment
