Atom Interferometer Gravimeter

Interferometer Settings

Local gravity g 9.81 m/s²

Pulse separation T 100 ms

Raman effective wavelength λ_eff 780 nm

Playback

Live Readout

P(|g⟩) = 100%P(|e⟩) = 0%

Fringe phase Δφ mod 2π

0.000 rad

Total phase k_eff·g·T² (unwrapped)

0 rad

Sensitivity |∂P/∂g|

0 s²/m

How it works

A cold-atom gravimeter measures g by turning free fall into a matter-wave interferometer. Each atom starts in ground state |g⟩ and internal momentum state, then meets three laser (Raman) pulses spaced by free-fall time T:

π/2 pulse (t=0) — puts the atom in a coherent superposition of |g⟩ and |e⟩, each carrying a different momentum kick ħk_eff. The wavepacket splits into two paths.
π pulse (t=T) — swaps the internal states, redirecting the two paths so they converge again.
π/2 pulse (t=2T) — recombines the paths and closes the interferometer.

Both paths fall identically under gravity (the trajectories are classical parabolas — this is Einstein's equivalence principle), but each laser pulse imprints a phase equal to k_eff times the atom's position at that instant. Because the atom is at a different height in each path when the middle pulse fires, the accumulated phase difference between the two arms is exactly:

Δφ = k_eff · g · T²
k_eff = 4π / λ_eff   (counter-propagating Raman beams)
P(|e⟩) = ½ [ 1 − cos(Δφ) ]
∂P/∂g = ½ · k_eff·T² · sin(Δφ)

The final population in |e⟩ is read out as a fringe: scanning g (or T) sweeps P through fringes. Because k_effT² is enormous compared to everyday phases (a few ms of free fall already wraps Δφ around 2π thousands of times), the sensitivity ∂P/∂g is huge — this is why atom interferometers reach μGal-level precision (~10⁻⁹ g) and are used for absolute gravity surveys, geodesy, and underground void/mineral detection. Real instruments resolve the 2π ambiguity by chirping the laser frequency to track a fringe as T is scanned; this simulator reads out only the single-shot fringe phase.

Controls: drag g to simulate different locations, T to change the free-fall time between pulses, λ_eff to change the momentum-transfer wavelength (smaller λ ⇒ larger k_eff ⇒ steeper fringes), or drop a fresh atom cloud at any time. The horizontal path separation shown is exaggerated for visibility — the real momentum-state paths differ by microns, but the vertical fall and every number in the readout panel are the exact physics.

PULSE

Path A (|g⟩) Path B (|e⟩) Raman laser

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