This is a 2D-native view of the same cold-atom gravimeter: rather than a 3D perspective scene, it draws the physics the way atom-interferometry papers actually plot it — a space-time worldline diagram, a quantum phasor, and a live fringe scan.
- Space-time diagram (top) — both paths fall identically under gravity (Einstein's equivalence principle), so this plot works in the free-falling frame and shows only the physical quantity that differs between the two paths: their two-photon-recoil-momentum separation. It opens linearly from 0 to vrT after the π/2 splitting pulse at t=0, then the π pulse at t=T swaps the momentum states so it closes symmetrically back to 0 at t=2T — the classic atom-interferometer "diamond".
- Phasor (bottom-left) — the quantum state's relative phase Δφ drawn as a vector on the unit circle; the projection onto the vertical axis is exactly cos(Δφ), the quantity the final π/2 pulse converts into a population difference.
- Fringe scan (bottom-right) — the analytic curve P(|e⟩)=½[1−cos(Δφ)] plotted against phase, with a marker at the current setting. Press "Scan g" to sweep g continuously and drop real Monte-Carlo single-shot outcomes (0 or 1, drawn with probability P(|e⟩) exactly like a real detector) onto the chart — watch the shot noise average out into the same cosine fringe.
k_eff = 4π / λ_eff
v_r = ħ·k_eff / m(87Rb) (real two-photon recoil velocity)
Δφ = k_eff · g · T² (same exact phase as the 3D sim)
P(|e⟩) = ½ [ 1 − cos(Δφ) ]
∂P/∂g = ½ · k_eff·T² · sin(Δφ)
Because keffT² is astronomically larger than everyday phases, Δφ wraps around 2π thousands of times even for a 100 ms drop — this is exactly why atom gravimeters reach μGal (10⁻⁹g) sensitivity: a tiny change in g produces a huge, easily-measured swing in the fringe. Real instruments resolve the 2π ambiguity by scanning g or T and tracking which fringe order they are on — press "Scan g" to see that scan build up on this page.