The arrow is a tiny magnet inside the diamond. A microwave "pushes" it around the ball. Pointing up means it glows brighter red; pointing down means a bit dimmer. With many arrows at once, each spins at a slightly different speed, so they spread out, unless you flip them all halfway through (that's the echo) and they line back up.

In the rotating frame a resonant drive rotates the spin about x at the Rabi frequency Ω; a detuning δ tilts the rotation axis to (Ω, 0, δ). During free time each spin precesses about z at its own δ. A Gaussian spread of static detunings gives the Ramsey decay exp(−(τ/T₂*)²); a π pulse in the middle of the free time reverses every spin's accumulated phase, which is the Hahn echo.

Ensemble of N two-level Bloch vectors (mₛ = 0, −1 subspace) with quasi-static detunings δᵢ ~ N(δ, σ), σ = √2/(2πT₂*). Pulses are exact rotations about (Ω cos φ, Ω sin φ, δᵢ); readout maps ⟨z⟩ to fluorescence with 30% contrast. The x–x–x echo returns the spin to mₛ = 0; experiments use a final −x or y pulse to map onto contrast. Same model as adamas.nv and the JavaScript is unit-tested (web/tests).