Fig. 1: Controllable splitting of a soliton into two daughter solitons by a repulsive Gaussian barrier.

a An example sequence of a soliton being split by the narrow barrier into two solitons of approximately equal atom number. The blue shaded region in the upper panel shows the signal obtained by integrating across the final image in the sequence. b The transmission of a soliton with a kinetic energy per atom of E_k/k_B = 15.5 ± 0.3 nK (black) and E_k/k_B = 41 ± 1 nK (red) through the wide barrier, as the barrier power is varied. The error bars are estimated from the distribution of repeated transmission measurements when the barrier is set to give equal splitting. The solid lines show the results of quasi-1D Gross–Pitaevskii equation (GPE) simulations using experimental parameters but with the barrier width extracted from a fit to the data, yielding values w_z = 11.28 ± 0.06 μm and w_z = 12.51 ± 0.09 μm, respectively. The grey shaded regions show quasi-1D GPE results with no fitted parameters and the extent of the region reflects the measured uncertainty in barrier width. c The barrier power required to achieve a transmission of 0.5 for both the narrow (blue) and wide (red) barriers. The values and uncertainties for the powers and kinetic energies are taken from fits to transmission curves (as in b) and trajectories of a soliton oscillating in the same harmonic potential without the barrier respectively. The straight lines are least-squares fits to the experimental data constrained to pass through the origin. The histogram in d shows the shot-to-shot variation in transmission for the narrow barrier, for a range of kinetic energies and barrier powers set to give an average transmission of 0.5. This histogram has a SD of 0.064. An equivalent histogram for the wide barrier has a SD of 0.085, which is represented in b by the vertical error bars.