Collision-induced frequency shifts in bright matter-wave solitons and soliton molecules

A recent experiment has detected collision-induced frequency shifts in bright matter-wave solitons for the first time [Nat. Phys. 10, 918 (2014)]. Using a particle model, we derive the frequency shift for two solitons in a harmonic trap, and compare it to the results of the recent experiment and reported theoretical approximation. We find regimes where the frequency shift is much smaller than previously predicted, and propose experiments to test these findings. We also predict that reducing the experimental trap frequency will reveal for the first time soliton molecules or soliton bound states in a cold atoms system. The dynamics of such bound states are found to be both highly phase-dependent, and sensitive to the residual 3D nature of the experiment.