The quantum mechanical description of a radiation field is based on states
that are characterized by the number of photons in a particular mode; the m
ost basic quantum states are those with fixed photon number, usually referr
ed to as number (or Fock) states. Although Fock states of vibrational motio
n can be observed readily in ion traps', number states of the radiation fie
ld are very fragile and difficult to produce and maintain. Single photons i
n multi-mode fields have been generated using the technique of photon pairs
(2,3). But in order to generate these states in a cavity, the mode in quest
ion must have minimal losses; moreover, additional sources of photon number
fluctuations, such as the thermal field, must be eliminated. Here we obser
ve the build-up of number states in a high-Q cavity, by investigating the i
nteraction dynamics of a probe atom with the field. We employ a dynamical m
ethod of number state preparation that involves state reduction of highly e
xcited atoms in a cavity, with a photon lifetime as high as 0.2 seconds. (T
his set-up is usually known as the one-atom maser or 'micromaser'.) Pure st
ates containing up to two photons are measured unambiguously.