We present exact results for the spectra of three fermionic atoms in a single well of an optical lattice. For the three lowest hyperfine states of 6Li atoms, we find a Borromean state across the region of the distinct pairwise Feshbach resonances. For 40K atoms, nearby Feshbach resonances are known for two of the pairs, and a bound three-body state develops towards the positive scattering-length side. In addition, we study the sensitivity of our results to atomic details. The predicted few-body phenomena can be realized in optical lattices in the limit of low tunneling.
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Luu et al. (2007) studied this question.
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