The same quantum coherence that a computer must protect makes an exquisite sensor. A single nitrogen-vacancy defect in diamond — one missing carbon next to a nitrogen atom — carries a spin-1 ground state whose levels shift in a magnetic field. Shine green light, sweep a microwave, and the field reads off directly as the frequency where the fluorescence dips. Below, the exact spin Hamiltonian is diagonalised as you turn up the field, through the anti-crossing at 102 mT and beyond.
The NV ground state is governed by a zero-field splitting $D=2.870$ GHz that separates the $m_s=0$ level from $m_s=\pm1$, plus a Zeeman term that a magnetic field adds along the defect axis. Diagonalising $H=D\,S_z^2+\gamma_e\,\mathbf{B}\!\cdot\!\mathbf{S}$ gives three levels; the two optically-detected resonances from the bright $m_s=0$ state sit at frequencies that move apart at $2\gamma_e$ per tesla — a transduction of $56.05$ GHz/T. Measuring that splitting is measuring the field.
The left panel traces the three ground-state levels as the field rises; the lower resonance falls until, at the ground-state level anti-crossing near 102 mT (where $\gamma_e B=D$), the $m_s=0$ and $m_s=-1$ levels meet. Tilt the field off the defect axis and that crossing opens into an avoided one. The right panel is the spectrum a microwave sweep would show at the current field: two dips whose separation reads the field. It is the same exact diagonalisation the library's high-field model uses to stay valid past the anti-crossing and into the 20-tesla regime.
Sensing is the mirror image of computing: both live or die by coherence, and the control that keeps a qubit's phase clean is the control that sharpens a sensor's line. The platform's magnetometry model shares the Hamiltonian machinery and the pulse-shaping toolbox with the rest of the portal — the difference is only what the phase is used for. It is also a reminder that a coupled-oscillator quantum device need not compute to be useful.
| Quantity | Value / role |
|---|---|
| Zero-field splitting $D$ | 2.870 GHz — separates $m_s=0$ from $m_s=\pm1$ |
| Gyromagnetic ratio $\gamma_e$ | 28.025 GHz/T — the field-to-frequency conversion |
| GSLAC | ground-state anti-crossing at $\gamma_e B=D$, ~102 mT |
| Transduction | $2\gamma_e=56.05$ GHz/T — splitting per unit field |
| Sensitivity floor | shot-noise-limited, sharpens with coherence time |
Evidence boundary: the panel diagonalises the exact NV ground-state spin-1 Hamiltonian live in your browser, its levels and ODMR frequencies checked against a NumPy reference to $2\times10^{-15}$ GHz. It is the library's simulation-only response model, valid through the anti-crossing into high field; it is not a measurement, and an instrument's absolute accuracy requires a separate NIST-traceable calibration.