Multiscale quantum-defect theory for two interacting atoms in a symmetric harmonic trap

We present a multiscale quantum-defect theory for two identical atoms in a symmetric harmonic trap that combines the quantum-defect theory for the van der Waals interaction [ B. Gao Phys. Rev. A 64 010701 (2001)] at short distances with a quantum-defect theory for the harmonic trapping potential at large distances. The theory provides a systematic understanding of two atoms in a trap, from deeply bound molecular states and states of different partial waves, to highly excited trap states. It shows, e.g., that a strong p-wave pairing can lead to a lower energy state around the threshold than a s-wave pairing.