Formation of matter-wave soliton molecules

Part of Focus on Modern Frontiers of Matter Wave Optics and Interferometry We propose an experiment for forming matter-wave soliton molecules. In the proposed setup, we show that if two solitons are initially prepared in phase and with a sufficiently small separation and relative velocity, a bound pair will always form. This is verified by direct numerical simulation of the Gross–Pitaevskii equation and by the derivation of the exact interaction energy of two solitons, which takes the form of a Morse potential. This interaction potential depends not only on the separation but also on the relative phase of the solitons and is essential for an analytical treatment of a host of other problems, such as the soliton gas and the Toda lattice of solitons.