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 [J. H. V. Nguyen et al., 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 recent experimental results 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 soliton molecules or soliton bound states in a cold-atom system. The bound-state dynamics are found to be both highly phase dependent and sensitive to the residual 3D nature of the experiment.