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The field is a frequency

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.

$$H = D\,S_z^{2} + \gamma_e\,B\,(\sin\theta\,S_x+\cos\theta\,S_z),\qquad D=2.870\ \mathrm{GHz},\quad \gamma_e=28.025\ \mathrm{GHz/T}$$
Live — the NV ground-state levels and its ODMR spectrum, exact diagonalisation
energy levels vs B GSLAC (102 mT) ODMR resonances
ODMR lines: , GHz splitting: GHz transduction: 56.05 GHz/T

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.

Deeper: shot-noise-limited sensitivity, and why coherence is the currency
How faint a field the magnetometer resolves is set by how sharply the resonance can be located, which is the shot-noise-limited sensitivity: for a Lorentzian line it carries a prefactor of $4/(3\sqrt3)$ (Barry et al., Rev. Mod. Phys. 2020) and scales with the linewidth over the contrast and the square root of the photon rate — so a narrower line, from a longer spin coherence time, buys sensitivity directly. That is the same $T_2$ a quantum computer fights to extend, spent here on precision instead of depth. This panel diagonalises the exact spin-1 Hamiltonian — its levels and ODMR frequencies matching a NumPy reference to $2\times10^{-15}$ GHz — but it is a simulation-only response model; an instrument's absolute accuracy needs a NIST-traceable calibration, a separate hardware-gated step.
Where it fits

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.

QuantityValue / 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
GSLACground-state anti-crossing at $\gamma_e B=D$, ~102 mT
Transduction$2\gamma_e=56.05$ GHz/T — splitting per unit field
Sensitivity floorshot-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.