Abstract
Bright solitons are non-dispersive wave solutions, arising in a diverse range of nonlinear, one-dimensional systems, including atomic Bose-Einstein condensates with attractive interactions. In reality, cold-atom experiments can only approach the idealized one-dimensional limit necessary for the realization of true solitons. Nevertheless, it remains possible to create bright solitary waves, the three-dimensional analogue of solitons, which maintain many of the key properties of their one-dimensional counterparts. Such solitary waves offer many potential applications and provide a rich testing ground for theoretical treatments of many-body quantum systems. Here we report the controlled formation of a bright solitary matter-wave from a Bose-Einstein condensate of (85)Rb, which is observed to propagate over a distance of ∼1.1 mm in 150 ms with no observable dispersion. We demonstrate the reflection of a solitary wave from a repulsive Gaussian barrier and contrast this to the case of a repulsive condensate, in both cases finding excellent agreement with theoretical simulations using the three-dimensional Gross-Pitaevskii equation.