Dipole-dipole interaction in optical cavities

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Abstract
At the most fundamental level of quantum electrodynamics, there is no such thing as two-body interactions between atoms. The potentials that describe these interactions are effective potentials resulting from a series of approximations whose validity depends on the precise situation at hand. Considering a one-dimensional geometry for simplicity, we discuss under which conditions the familiar form of the near-resonant dipole-dipole interaction is valid, paying particular attention to the effects of interatomic propagation of light, and to what extent it can be modified in the tailored electromagnetic environments provided by optical resonators. We find that once the atoms have established that they are inside a resonator, the dipole-dipole potential may or may not remain a useful concept, depending upon the strength of the atom-field interaction. In the weak-coupling regime, one finds a two-body dipole-dipole interaction that can be enhanced or inhibited by varying the atom-field detuning. In the strong-coupling regime, by contrast, the two-body dipole-dipole potential ceases to be meaningful.

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