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Summary form only given. A new regime in cavity QED is realized in which single atoms interact with the cavity field for very long times (i.e., many Rabi cycles) and in which the atomic kinetic energy is comparable to or smaller than the dipole coupling energy. The mechanical effects of just a few-photon light field should therefore enable single atoms to be trapped in effective potential wells. We consider such a situation in the far detuned dispersive regime of cavity QED, where a single atom is confined in the lower (quantized) bound states of the effective optical potential formed around an antinode of the standing wave cavity field.