Quantum State Control via Trap-induced Shape Resonance in Ultracold Atomic Collisions

We investigate controlled collisions between trapped but separated ultracold atoms. The interaction between atoms is treated self-consistently using an energy-dependent delta-function pseudopotential model, whose validity we establish. At a critical separation, a trap-induced shape resonance between a molecular bound states and a vibrational eigenstate of the trap can occur. This resonance leads to an avoided crossing in the eigenspectrum as a function of separation. We investigate how this new resonance can be employed for quantum control.