This is the Colella–Overhauser–Werner (COW) experiment (1975): a single silicon crystal, cut into three thin parallel slabs, splits a neutron beam by Bragg diffraction into two coherent paths that enclose a small area, then recombines them. Rotating the whole crystal about the beam axis by angle φ tilts that enclosed loop against gravity, lifting one path and dropping the other by an amount ∝ sin φ — the dial in the top panel is that rotation, viewed end-on along the beam; drag it (or the slider) to tilt the crystal.
Δφ = 2π·m²·g·λ·A·sin φ / h² ≡ m²·g·λ·A·sin φ / (2π·ħ²)
m = neutron mass (1.675×10⁻²⁷ kg)
g = local gravity
λ = de Broglie wavelength of the neutron
A = area enclosed by the two interfering paths
h = Planck constant, ħ = h/2π
Numerical note: a widely-copied shorthand for this formula drops the h→ħ conversion's 2π incorrectly and writes Δφ = m²gλA·sinφ/ħ² (no 2π at all). Checked against this simulator's own parameters (λ=1.4 Å, A=8 cm², Earth g, φ=90°), that shorthand predicts a phase of ≈88.2π — about 44 full fringes swept in a single quarter-turn, which contradicts the qualitative "a few fringes per turn" behaviour the original 1975 apparatus actually showed. The standard textbook/Wikipedia form used above (with the 2π restored) gives ≈14.0π for the same inputs — an order of magnitude fewer fringes, consistent with the real experiment. This simulator uses the corrected 2π form.
The two paths pick up a relative quantum phase Δφ purely from gravity acting on their matter wave — no classical force ever touches the neutron between the plates. That phase shows up directly as an oscillation in the two exit-beam count rates:
I_O = I₀/2 · (1 + V·cos Δφ) forward "O-beam"
I_H = I₀/2 · (1 − V·cos Δφ) diffracted "H-beam"
- Dial / φ slider — tilts the crystal about the beam axis; the middle panel's path separation and the bottom-left fringe curve trace out the same sin φ dependence.
- λ and A sliders — a longer wavelength or a larger enclosed loop packs more fringes into the same tilt range, since Δφ scales linearly with both; λ also sets the neutrons' speed (v = h/mλ), so longer wavelengths visibly slow the dots in the middle panel.
- Visibility V — models contrast loss from real crystal imperfections; the bottom-right phasor diagram shows it directly as the length of the tilted (path II) vector.
- Gravity — set it to zero and the two beams stop oscillating entirely: the fringe pattern is a direct, uncontroversial demonstration that gravity couples to a quantum matter wave's phase, not just to classical trajectories.