Interacting atoms under strong quantum confinement

We calculate the energy-level shifts of a tightly confined trapped alkali-metal atom in the presence of a second trapped atom. A complete microscopic description of the interaction energy between the two atoms is used. This allows us to study tightly confined atoms near a Feshbach resonance and to evaluate the usefulness of the regularized $\delta$-function potential approximation. We present results for sodium and cesium when confined in a spherically symmetric harmonic optical trap. Possible implications of the level shifts and collisional decoherence for quantum computing with atomic systems are given.