Fig. 1: Caustic networks from two repulsive potentials in an atom laser.

a Experimental data averaged over 15 runs. The atom laser propagates from top (z = 0) to bottom. Each barrier is Gaussian-shaped [Eq. (2)] with U₀/k_B = 23.1 μK and σ = 10.3 μm. The left barrier is positioned h = 85 μm below the injection point of the atoms (ε = 0.95, see Eq. (3)). The right barrier is offset from this by (Δx, Δz) = (39, −42) μm (ε = 0.64). b A numerical rendering of the classical trajectories as a sheet \(({x}_{i},{t}_{i})\mapsto (x,z,{t}_{i}-\sqrt{-2z/{a}_{z}})\), the singularities of which appear as caustics when projected down into the (x, z) imaging plane where the experimental data is shown again. Here, t is the vertical direction, while x increases to the left, and z decreases into the image. Red shading denotes regions where \(\det {{{{{{{{\bf{J}}}}}}}}}^{-1}\) is large [Eq. (1)], corresponding to the caustics when projected onto the imaging plane. c A numerical rendering of the classical trajectories as a sheet (x_i, t_i) ↦ (x, z, t_i), which now includes the free-fall background.