Tunneling dynamics of two interacting one-dimensional particles

Motivated by recent cold atom experiments, the time evolution of two one-dimensional particles with attractive or repulsive short-range interaction is considered. We treat a realistic trapping potential that consists of an approximately harmonic optical trap plus a linear magnetic field gradient. This provides an ``inside region,'' where the particles are trapped, and an ``outside region,'' where the particles are free. When the barrier, which separates the two regions, is high enough, tunneling is suppressed. When the barrier is lowered, the time evolution of the system results in the loss of atoms from the trap. We find that pair tunneling dominates for strongly attractive interactions, while single-particle tunneling dominates for weak interactions.