  The quantum properties of electromagnetic, mechanical or other harmonic
oscillators can be revealed by investigating their strong coherent coupling to
a single quantum two level system in an approach known as cavity quantum
electrodynamics (QED). At temperatures much lower than the characteristic
energy level spacing the observation of vacuum Rabi oscillations or mode
splittings with one or a few quanta asserts the quantum nature of the
oscillator. Here, we study how the classical response of a cavity QED system
emerges from the quantum one when its thermal occupation -- or effective
temperature -- is raised gradually over 5 orders of magnitude. In this way we
explore in detail the continuous quantum-to-classical crossover and demonstrate
how to extract effective cavity field temperatures from both spectroscopic and
time-resolved vacuum Rabi measurements.
