In fact, of course, the photon number does not increase without limit as atoms keep crossing the resonator. Because the walls are not perfect reflectors, the more photons there are, the greater becomes the chance that one of them will be absorbed. Eventually this loss catches up to the gain caused by atomic injection.
About 100,000 atoms per second can pass through a typical micromaser (each remaining perhaps 10 microseconds); meanwhile the photon lifetime within the cavity is typically about 10 milliseconds. Consequently, such a device running in steady state contains about 1,000 microwave photons. Each of them carries an energy of about 0.0001 electron volt; thus, the total radiation stored in the cavity does not exceed one tenth of one electron volt. This amount is much smaller than the electronic excitation energy stored in a single Rydberg atom, which is on the order of four electron volts.
Although it would be difficult to measure such a tiny field directly, the atoms passing through the resonator provide a very simple, elegant way to monitor the maser. The transition rate from one Rydberg state to the other depends on the photon number in the cavity, and experimenters need only measure the fraction of atoms leaving the maser in each state. The populations of the two levels can be determined by ionizing the atoms in two small detectors, each consisting of plates with an electric field across them. The first detector operates at a low field to ionize atoms in the higher-energy state; the second operates at a slightly higher field to ionize atoms in the lower-lying state (those that have left a photon behind in the cavity).
With its tiny radiation output and its drastic operational requirements, the micromaser is certainly not a machine that could be taken off a shelf and switched on by pushing a knob. It is nevertheless an ideal system to illustrate and test some of the principles of quantum physics. The buildup of photons in the cavity, for example, is a probabilistic quantum phenomenon-- each atom in effect rolls a die to determine whether it will emit a photon-- and measurements of micromaser operation match theoretical predictions.
An intriguing variation of the micromaser is the two-photon maser source. Such a device was operated for the first time five years ago by our group at ENS. Atoms pass through a cavity tuned to half the frequency of a transition between two Rydberg levels. Under the influence of the cavity radiation, each atom is stimulated to emit a pair of identical photons, each bringing half the energy required for the atomic transition. The maser field builds up as a result of the emission of successive photon pairs.
The presence of an intermediate energy level near the midpoint between the initial and the final levels of the transition helps the two-photon process along. Loosely speaking, an atom goes from its initial level to its final one via a "virtual" transition during which it jumps down to the middle level while emitting the first photon; it then jumps down again while emitting the second photon. The intermediate step is virtual because the energy of the emitted photons, whose frequency is set by the cavity, does not match the energy differences between the intermediate level and either of its neighbors. How can such a paradoxical situation exist? The Heisenberg uncertainty principle permits the atom briefly to borrow enough energy to emit a photon whose energy exceeds the difference between the top level and the middle one, provided that this loan is paid back during the emission of the second photon.
Like all such quantum transactions, the term of the energy loan is very short. Its maximum duration is inversely proportional to the amount of borrowed energy. For a mismatch of a few billionths of an electron volt, the loan typically lasts a few nanoseconds. Because larger loans are increasingly unlikely, the probability of the two-photon process is inversely proportional to this mismatch.