IN33 · Read a magnetic field from dimmer fluorescence

NV-center magnetometer

How can a dimmer diamond reveal the direction of a magnetic field? Microwaves dim the fluorescence when their frequency matches a spin transition. A magnetic field splits the transitions differently along each diamond axis. Several known axes and a known bias can determine a local field vector. A common frequency shift also responds to temperature and strain.

Rotate a magnetic source and retain a counted microwave sweep. Separate common resonance drift from a field inferred with independently measured references.

A field changes the resonance pair

Conditional field increment $65\,\mathrm{\mu T}$

Inferred azimuth $35^\circ$

Common splitting drift $0\,\mathrm{MHz}$

Withheld field check error $0.8\,\mathrm{\mu T}$

Orientation modelField azimuth input

\phi_{\mathrm{in}}/{}^\circ

35

Objective collection half-angle

\alpha/{}^\circ

25

Hold the gold source handle to turn the field. Single-axis mode changes its axial amplitude.

Timing, source and inference assumptions

Source field amplitude

B_{\mathrm{in}}/\mathrm{\mu T}

Temperature offset input

\Delta T_{\mathrm{in}}/\mathrm K

Field tilt input

\theta_{\mathrm{in}}/{}^\circ

Count gate per frequency

\tau_{\mathrm{gate}}/\mathrm s

Individual hyperfine linewidth

\Gamma/\mathrm{MHz}

Synthesizer frequency scale

a_f

Synthesizer frequency offset

b_f/\mathrm{MHz}

Transverse strain input

E/\mathrm{MHz}

Count seed

s

Known magnetic biasStrain interpretation

Changing frequency hardware or collection acquires fresh references. The unknown norm is limited to 150 microteslas around the known bias.

Model assumptions

Continuous green pumping and weak microwave driving give phenomenological Lorentzian fluorescence dips. A complete electronic spin-one Hamiltonian retains transverse fields; each transition has an equal-population secular nitrogen-14 triplet with 2.16 megahertz spacing. Nuclear transverse mixing, charge dynamics and a pumping master equation are omitted. Two gated frequency-counter references, a dark exposure and a known-biased diamond sweep are acquired separately. A third counter reading and a known magnetic increment are withheld checks. The four-axis inverse is conditional on a known crystal frame, stable zero transverse strain, the applied bias and an unknown increment within 150 microteslas. It uses counted line-group fits, not generator labels. Without bias, unsigned spectra cannot select one vector. Single-axis mode assumes an axial increment and reports only that component. Common splitting drift mixes temperature with axial strain; a temperature conversion additionally assumes stable axial strain. A declared strain change withholds field conclusions. Photon counts use exact low-count Poisson and a normal approximation above forty; detector occupancy must remain below one percent. Geometric collection uses an air-side equivalent isotropic point source and fixed efficiency; internal refraction and total internal reflection are omitted. Optical polarization, aberration, loss fluctuations and quantum-limited sensitivity are not inferred. A remote ideal dipole sets the field at the single sensor point. Known bias sources are represented by their supply; uniform bias is independently specified. Crystal and NV details are enlarged, supports and ray brightness schematic. Spectra remain below the apparatus.

Simulated detector counts · retained frequency gates

The resonance is a dip in photon counts

One fluorescence signal supplies these counts. The enlarged NV structure is a model.

Inspect record

Counted frequency sweep · zoomed count scale

$N/(10^3\,\mathrm{photon})$

$f/\mathrm{MHz}$

Observed countsOne joint fitted spectrum

References, timing and every counted gate

The counter sees one collected fluorescence signal. The curve below is fitted to its saved counts; the enlarged NV structure above is a model.

Counter-based frequency calibration

f=a_f f_{\mathrm{cmd}}+b_f

Measured reference splitting

D_{\mathrm{ref}}=2870\,\mathrm{MHz}

Fitted individual hyperfine linewidth

\Gamma=1.2\,\mathrm{MHz}

Raw synchronous frequency gates and photons
$f_{\mathrm{cmd}}/\mathrm{MHz}$	$t_{\mathrm{start}}/\mathrm s$	$t_{\mathrm{end}}/\mathrm s$	$N/\mathrm{photon}$

Each frequency is held for its recorded gate. The animation replays gates faster than acquisition time; it is not a new measurement. The clock starts at instrument time zero. CSV retains sample, reference and withheld check scans, frequency-counter pulse totals and gates, dark counts, axes, bias, versions, units, seeds and flags.

Separate generating reference

The input field and temperature describe the synthetic source. They do not enter the inverse or raw CSV/JSON.

\lVert\mathbf B_{\mathrm{in}}\rVert=65\,\mathrm{\mu T}

Hamiltonian, branch assumptions and primary sources

H/h=D S_z^2+\gamma\mathbf B\cdot\mathbf S+E(S_x^2-S_y^2)

\begin{aligned}\sqrt3\,\mathbf n_1&=(1,1,1),\\\sqrt3\,\mathbf n_2&=(1,-1,-1),\\\sqrt3\,\mathbf n_3&=(-1,1,-1),\\\sqrt3\,\mathbf n_4&=(-1,-1,1).\end{aligned}

The complete electronic spin matrix retains transverse fields. Each electronic group is a symmetric equal-population nitrogen-14 triplet, spaced by 2.16 megahertz; transverse nuclear mixing and unequal nuclear populations are omitted. Fluorescence uses a weak-CW Lorentzian model. The four-axis fit is local to a measured known-bias reference, with an increment norm at most 150 microteslas and stable zero transverse strain. The single-axis unknown is assumed axial.

A common zero-field splitting shift can mean temperature or axial strain. A conditional temperature estimate assumes stable axial strain; no sensitivity or certified uncertainty is inferred. Azimuth is hidden below a conservative five-microtesla display guard, not a sensitivity specification. Photon sampling uses a normal approximation above forty. The low-rate detector model neglects dead-time correction only below one percent occupancy; shot noise is included, laser drift and calibration systematics are not. The 532-nanometre excitation and red fluorescence pass through ideal finite optics. Collection uses an air-side equivalent isotropic point source and fixed efficiency; internal refraction and total internal reflection are omitted. The remote source is an ideal dipole; external bias hardware is shown by its supply. Crystal scale, photon animation and mechanical supports are schematic.

Start with the essentials

Focus question: Which information fixes a field component, and which information is needed for a vector?
One-sentence intuition: The two branches separate magnetic splitting from common drift; a vector also needs independently known axes and a resolved bias branch.

Core mathematical model

Electronic spin Hamiltonian

H/h=D S_z^2+\gamma\mathbf B\cdot\mathbf S+E(S_x^2-S_y^2)

The local quantization direction follows an NV axis. The zero-field and strain parameters describe the electronic level structure. The instrument diagonalizes the full electronic matrix; nuclear dynamics are represented only by a declared secular triplet.

Axial small-field limit

f_\pm\simeq D\pm\gamma B_\parallel,\qquad\gamma=0.028\,\mathrm{MHz/\mu T}

Half the separation gives an axial projection in this limit. A common midpoint shift can come from temperature or axial strain. Transverse fields add shifts that the vector calculation retains.

A finite collection cone

\eta_\Omega=\frac{1-\cos\alpha}{2}

This fraction follows air-side equivalent isotropic point emission; internal diamond refraction is omitted. It gives the fraction entering the stated objective cone. A fixed detector efficiency and a separately counted dark rate complete the synthetic counting chain.

Common difficulties

Brightness and frequency

Typical misconceptionDarker light means a stronger magnetic field.

Better mental modelBrightness also depends on collection, pumping and contrast. Resonance frequencies, fitted from counts, carry the field information.

Axis and sign information

Typical misconceptionEight spectral groups uniquely identify a vector in any orientation.

Better mental modelUnsigned frequencies permit sign and axis ambiguities. This inverse uses a known crystal frame, a measured reference under known bias and a bounded local increment.

Shared shifts

Typical misconceptionEvery shared shift measures temperature.

Better mental modelTemperature and axial strain both shift the zero-field splitting. The conversion needs an additional stable-strain assumption.

Run the experiment

01
Follow the light
Use the sensor view and identify the diamond, objective, red filter and photon counter.
What to observe: Green excitation reflects toward the specimen. Red fluorescence passes through the dichroic and reaches one finite detector face.
02
Rotate the source
Hold the gold source handle and move it horizontally.
What to observe: The actual source moment and its field at the diamond change. A fresh counted spectrum gives different line-group positions.
03
Compare one axis with four
Choose the single-axis preset and then the vector preset.
What to observe: The single-axis result is conditional on an axial unknown. Four axes add independent projections within the known-bias branch.
04
Separate drift from splitting
Choose the thermal-shift preset.
What to observe: The groups move together as well as retaining magnetic separation. The inferred common zero-field splitting shift has a temperature interpretation only if axial strain is stable.
05
Remove an assumption
Remove the bias, then inspect the strain challenge.
What to observe: The raw counts remain visible while a unique field conclusion is withheld.
06
Keep and replay
Keep one cycle, change the source, and select the earlier record before exporting CSV.
What to observe: Earlier counts and their references remain unchanged. CSV includes the complete sample, reference and withheld sweep plus frequency-counter and dark records.

NV-center magnetometer

The resonance is a dip in photon counts

Read frequency before interpreting a field

Core mathematical model

Electronic spin Hamiltonian

Axial small-field limit

A finite collection cone

Common difficulties

Brightness and frequency

Axis and sign information

Shared shifts

Run the experiment

Follow the light

Rotate the source

Compare one axis with four

Separate drift from splitting

Remove an assumption

Keep and replay

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