IN34 · Read the spin rhythm

Optically Pumped Magnetometer

How can light read atomic precession without mistaking brightness drift for a magnetic field? A magnetic field sets the atomic precession frequency. A weak probe turns that motion into a changing polarization; two optical channels and an independent brightness monitor separate common probe drift. Pump drift changes the spins themselves and needs a separate check.

Drive polarized cesium spins with an RF field and sweep through resonance. Compare two counted optical channels, probe drift and the separate static weak-field response.

A field sets the spin rhythm

Hold the gold bias dial and drag. Each change acquires a new preview; kept records retain their own standards.

Inferred field $200\,\mathrm{nT}$

Absorptive full width $23\,\mathrm{Hz}$

Optical response RMS $3.4\,\mathrm{mrad}$

Relative fit residual $0.018$

Measurement branchBias field

B/\mathrm{nT}

200

Pump rate

R/\mathrm{s}^{-1}

45

RF peak field

B_1/\mathrm{nT}

1.5

Pump–field angle

\theta/{}^{\circ}

20

Optical axes, drift and counting

Probe tilt toward field

0

RF tilt toward field

0

Probe brightness factor

1

Probe drift across sweep

0

Pump drift across sweep

0

Optical signal phase delay

0

Counting seed

3401

Photon counting noise

Model assumptions

Synthetic two-beam cesium ground-state orientation model with isotropic Bloch relaxation. Mx uses the rotating-wave approximation, a linearly driven RF field and its co-rotating half amplitude; the static branch solves the RF-off equation directly. All rates, fluxes, optical gain and geometry are teaching assumptions. A weak non-perturbing probe rotates in proportion to spin projection; count noise uses a Poisson law below sixty photons and a normal approximation above it. Gate-averaged rotation precedes the nonlinear analyzer. Inference requires a known frequency scale, dark and rotation standards, stable pump, supported geometry and a resolved line; the static field is conditional on known relaxation and the stated monotonic branch. No SERF, spin-exchange collision dynamics, hyperfine mixing, light shifts, spatial gradients, temperature physics, vector reconstruction or manufacturer sensitivity is modeled. Scene dimensions are schematic millimetres; spin arrows, photons and precession speed are enlarged or slowed.

Display record

Signed response from simulated photon gates

Cosine channel $X$ Negative-sine channel $Y$

$f/\mathrm{Hz}$ · $\varphi/\mathrm{mrad}$

Retained detector counts at the strongest response

Collector ACollector B

$t/\mathrm{ms}$ · photons per gate

Standards, blanks and inference conditions

CSV retains every time gate, two detectors, probe and pump monitors, signed references, frequency or coil readback, dark observations and three known analyzer angles. The fit reads these observations only. Mx fits a common centre and absorptive width with nuisance amplitudes and phases. Static inference assumes independently known pumping and relaxation and stays inside the monotonic branch.

First eight raw gates of the selected record
Gate	$t_0/\mathrm{s}$	A	B	Probe monitor	Pump monitor

Separate synthetic ideal reference

The ideal reference is generating context stored separately in JSON. It is excluded from the raw CSV and from every inference.

Start with the essentials

Focus question: How can light read atomic precession without mistaking brightness drift for a magnetic field?
One-sentence intuition: A normalized detector pair cancels common probe brightness; pumping changes spin orientation and relaxation and needs its own monitor.

Core mathematical model

Spin orientation dynamics

\dot{\mathbf P}=\mathbf P\times\gamma_F\mathbf B-\Gamma_0\mathbf P+R(\mathbf k_p-\mathbf P)

Torque sets precession, relaxation removes orientation, and the pump replenishes it along the optical axis. Pumping also increases the total relaxation rate. Rates and optical gain are declared teaching assumptions.

A cesium frequency scale at low field

f_L=\frac{\gamma_F}{2\pi}|\mathbf B|,\qquad\frac{\gamma_F}{2\pi}=3.4986\,\mathrm{Hz/nT}

One ground-state hyperfine manifold is selected. A resolved resonance centre becomes a field magnitude through the known gyromagnetic ratio.

Signed quadratures follow IN13

X=\sqrt2\langle\varphi\cos\psi\rangle,\qquad Y=-\sqrt2\langle\varphi\sin\psi\rangle

Dark observations and independent rotation standards convert the detector counts to rotation. The saved cosine and negative-sine references then give RMS-scaled signed channels. A cosine signal leading the reference gives positive quadrature.

A separate static low-field branch

P_x=-\frac{R\gamma_F B_y}{(\Gamma_0+R)^2+(\gamma_F B_y)^2}

RF is off, the pump points along the positive longitudinal axis and the field is transverse. Rotation is approximately linear near zero and eventually turns over. Inference uses only the declared monotonic interval.

Common difficulties

What normalization removes

Typical misconceptionNormalization removes every laser-power change.

Better mental modelCommon probe brightness multiplies both outputs and can cancel. Pump power changes the spins and linewidth, so it needs a separate check.

Zero field and rotating waves

Typical misconceptionSetting the resonance frequency to zero makes a zero-field magnetometer.

Better mental modelThe rotating-wave approximation needs sufficiently fast precession. The static branch solves the RF-off equation directly; collision physics for SERF is absent.

Run the experiment

01
Drag the field dial
Hold the gold bias dial and drag horizontally.
What to observe: The resonance centre moves with the field; the spin arrow and newly acquired counts update during the drag.
02
Compare two drifts
Choose Probe brightness drifts, then Pump power drifts.
What to observe: Normalization preserves the resonance under common probe drift. The independent pump monitor detects pump drift and withholds a stationary inference.
03
Find a directional dead zone
Choose Look along the field, then return to Driven precession.
What to observe: A probe along the static field cannot see transverse precession. Photon counts remain available, but the magnetic conclusion is withheld.
04
Try the static branch
Choose Static weak field and slowly change the bias field.
What to observe: With RF off, rotation changes across the calibrated coil sweep. Leaving the monotonic branch withholds a unique field.
05
Keep and replay
Keep a sweep, change pumping, select the earlier record and export CSV.
What to observe: Its time gates, standards and counts stay fixed. The CSV contains no generating field and can still reproduce the inference.

Optically Pumped Magnetometer

Signed response from simulated photon gates

Static optical rotation from counted gates

Retained detector counts at the strongest response

Read a spin rhythm with light

Core mathematical model

Spin orientation dynamics

A cesium frequency scale at low field

Signed quadratures follow IN13

A separate static low-field branch

Common difficulties

What normalization removes

Zero field and rotating waves

Run the experiment

Drag the field dial

Compare two drifts

Find a directional dead zone

Try the static branch

Keep and replay

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