Abstract

There has been great progress over the last decade in experiments with one, or a few atoms, interacting with a single mode of the electromagnetic field. The basic theory of such systems is straightforward and was worked out long ago. Today, with the help of a computer, it is possible to add to the basic theory such things as the spatial variation of the dipole coupling constant for a moving atom, dispersion in the velocities of the atoms in an atomic beam, spontaneous emission, cavity loss and the interaction with residual thermal fields, etc.. The situation for what can be done with computers changes quickly, however, when the number of atoms interacting simultaneously with the field is increased. There are, moreover, many situations in cavity QED where multi-atom effects must be taken into account. For example, in the case of a standing-wave TEM₀₀ mode crossed by a thermal atomic beam, even if there is just one atom (on average) within the mode waist, it may still be desirable to include ten to twenty atoms in a calculation [1]. Another example is found in the recent measurements of photon statistics in cavity QED [2] where there are on the order of ten atoms within the mode waist; it is desirable in this case to make the calculations with something like one hundred atoms; then, even if two-state atoms are assumed, the Hilbert space for the internal degrees of freedom has a dimension of 10³⁰ and the brute force numerical approach becomes unthinkable.

© 1998 IEEE