Fig. 5: Sensitivity of the interferometer output to the barrier position.

a The fraction of atoms on the right of the narrow barrier following the second barrier interaction, as a function of barrier offset. The data points and error bars show the means and SDs across five to ten measurements taken at each offset position. The blue shaded region displays the maximum and minimum values at each offset position. The single green point and horizontal error bar indicate the independently measured shot-to-shot variation in the barrier position. The red oscillatory curve shows the result of a quasi-1D Gross–Pitaevskii equation (GPE) simulation based on experimental parameters, with the thickness reflecting the experimentally determined uncertainty in the barrier width. The kinetic energy of the soliton per atom at the barrier is E_k/k_B = 2.4 ± 0.2 nK. b, c Histograms compiled from the experimental data in a, for offsets larger than 5 μm and less than 1.3 μm, respectively. These histograms have SDs of 0.086 and 0.22, respectively. d, e Equivalent histograms sampled stochastically from quasi-1D GPE simulations, assuming a 1.3 μm uncertainty in the barrier offset. They have SDs of 0.041 and 0.16, respectively.