Figure 2: Timeline of the proposed experiment and snapshots of the collisional halo from the numerical simulations.

In panel a, time t=0 corresponds to the coherent splitting of the source condensate that sets up the collision; V_L(t) denotes the depth of the lattice potential formed by the Bragg lasers, with the first hump indicating the mirror (π) pulse, whereas the second hump indicates the beam-splitter (π/2) pulse (the initial source-splitting pulse is not shown for clarity). Panels b–d show the results of numerical simulations of the momentum-space density distribution n(k) of scattered atoms on the equatorial plane of the halo; panel b shows the density distribution after the collision, at t₁=65 μs; (c) shows the density distribution after the π-pulse, centred at t₂=75 μs and having a duration of τ_π=2.5 μs (r.m.s. width of Gaussian envelope); and (d) shows the density distribution after the final π/2-pulse, with Δt_free=t₃−t₂=85 μs and τ_π/2=2.5 μs (see Methods for further details; the durations shown on the time axis are not to scale). The momentum axes k_x,y in panels b–d are normalized to the collision momentum k₀≡|k₀| (in wave-number units), which in our simulations was k₀=4.7 × 10⁶ m⁻¹. The simulations were carried out for an initial BEC containing a total of N=4.7 × 10⁴ atoms of metastable helium (⁴He*), prepared in a harmonic trap of frequencies (ω_x, ω_y, ω_z)/2π=(64, 1150, 1150) Hz, and colliding with the scattering length of a=5.3 nm; all these parameters are very close to those realised in recent experiments^7,8.