A nitrogen-vacancy (NV) centre is a point defect in diamond whose electron spin resonance frequency shifts under a magnetic field (the Zeeman effect). In bulk diamond, NV defects sit along four distinct ⟨111⟩ crystal directions with no preferred one, so an ensemble of NV centres reports four independent measurements of the same field:
Δf_i = 2·γ·|B · n̂_i| (i = 1..4)
γ ≈ 28 MHz/mT (0.028 MHz/µT)
n̂_i = the four ⟨111⟩-type unit vectors
Each axis's ODMR spectrum shows two dips split by Δf_i, proportional to the field's projection onto that axis only (not the full vector). Because the four axes are non-coplanar, their four projections over-determine the three unknown components of B: a least-squares fit over the ±1 sign choices for each projection recovers the full 3D vector.
- |B|, θ, φ sliders — set the true applied field in spherical coordinates; the white arrow is the true vector, the four colored arrows are the fixed NV crystal axes.
- Per-axis bars — the Zeeman splitting each axis actually measures, in MHz. Only magnitude is directly observable, not sign.
- Add readout noise — adds photon-shot-noise-like Gaussian jitter to each splitting before reconstruction, so the recovered vector (orange arrow) visibly wobbles off the true one, same as a real ODMR measurement with finite averaging time.
- The overall global sign of B is fundamentally unresolvable from |projections| alone (flipping the whole field flips all splittings' signs, leaving |Δf_i| unchanged) — real magnetometers break this with a small known bias field. The display fixes the sign to match the true field for clarity.
Real-world relevance: this four-axis reconstruction is exactly how diamond-based vector magnetometers (used in biomagnetic imaging, current sensing, and geophysics) recover a full 3D field from a single crystal, without any moving parts.