Conditions of Low Dimensionality for Strongly Interacting Atoms Under a Transverse Trap

For a dilute atomic gas in a strong transverse trapping potential, one normally expects that, in the ground state, the gas will populate only the lowest transverse level. We show, however, that for the strongly interacting gas under a Feshbach resonance, the ground state includes a large fraction of atoms in excited levels of the trap, even if the gas is very dilute and the trap is very strong. This is because the effective atom-molecule coupling is typically enhanced to many times the trap mode spacing by an induced confinement along the untrapped dimension(s). Thus one cannot ''freeze out'' the transverse degrees of freedom except under certain conditions.