One could inject perhaps a dozen or so photons into a cavity and then launch through it, one by one, Rydberg atoms whose velocity is fixed at about a meter per second. The kinetic energy of these atoms would be greater than the atom-cavity potential energy, and they would pass through the cavity after experiencing a slight positive or negative delay, depending on the sign of the atom-cavity detuning. To detect the atom's position after it has passed through the cavity, researchers could fire an array of field ionization detectors simultaneously some time after the launch of each atom. A spatial resolution of a few microns should be good enough to count the number of photons in the cavity.
Before measurement, of course, the photon number is not merely a classically unknown quantity. It also usually contains an inherent quantum uncertainty. The cavity generally contains a field whose description is a quantum wave function assigning a complex amplitude to each possible number of photons. The probability that the cavity stores a given number of photons is the squared modulus of the corresponding complex amplitude.
The laws of quantum mechanics say that the firing of the detector that registers an atom's position after it has crossed the cavity collapses the ambiguous photon-number wave function to a single value. Any subsequent atom used to measure this number will register the same value. If the experiment is repeated from scratch many times, with the same initial field in the cavity, the statistical distribution of photons will be revealed by the ensemble of individual measurements. In any given run, however, the photon number will remain constant, once pinned down.
This method for measuring the number of photons in the cavity realizes the remarkable feat of observation known as quantum nondemolition. Not only does the technique determine perfectly the number of photons in the cavity, but it also leaves that number unchanged for further readings.
Although this characteristic seems to be merely what one would ask of any measurement, it is impossible to attain by conventional means. The ordinary way to measure this field is to couple the cavity to some kind of photodetector, transforming the photons into electrons and counting them. The absorption of photons is also a quantum event, ruled by chance; thus, the detector adds its own noise to the measured intensity. Furthermore, each measurement requires absorbing photons; thus, the field irreversibly loses energy. Repeating such a procedure therefore results in a different, lower reading each time. In the nondemolition experiment, in contrast, the slightly nonresonant atoms interact with the cavity field without permanently exchanging energy.
Quantum optics groups around the world have discussed various versions of quantum non-demolition experiments for several years, and recently they have begun reducing theory to practice. Direct measurement of an atom's delay is conceptually simple but not very sensitive. More promising variants are based on interference effects involving atoms passing through the cavity--like photons, atoms can behave like waves. They can even interfere with themselves. The so-called de Broglie wavelength of an atom is inversely proportional to velocity; a rubidium atom traveling 100 meters per second, for example, has a wavelength of 0.45 angstrom.
If an atom is slowed while traversing the cavity, its phase will be shifted by an angle proportional to the delay. A delay that holds an atom back by a mere 0.22 angstrom, or one half of a de Broglie wavelength, will replace a crest of the matter wave by a trough. This shift can readily be detected by atomic interferometry.
If one prepares the atom itself in a superposition of two states, one of which is delayed by the cavity while the other is unaffected, then the atomic wave packet itself will be split into two parts. As these two parts interfere with each other, the resulting signal yields a measurement of the phase shift of the matter wave and hence of the photon number in the cavity. Precisely this experiment is now under way at our laboratory in Paris, using Rydberg atoms that are coupled to a superconducting cavity in an apparatus known as a Ramsey interferometer.