---
title: "Optically Pumped Magnetometer Interactive Lab | Sandbox Physics"
description: "How can light read atomic precession without mistaking brightness drift for a magnetic field? A magnetic field sets the atomic precession frequency."
canonical_url: "https://sandboxphysics.com/labs/optically-pumped-magnetometer/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/optically-pumped-magnetometer/"
last_modified: "2026-11-12"
---

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.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

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 A Collector 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.

Physics tutorial

## Read a spin rhythm with light

**Background** Circular pump light orients cesium spins. A transverse RF field drives their precession, and a weak probe reads the resulting optical rotation.

**Why it matters** The detectors count photons. A field interpretation needs to distinguish atomic motion from changes in the light source.

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 misconception** Normalization removes every laser-power change.

**Better mental model** Common 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 misconception** Setting the resonance frequency to zero makes a zero-field magnetometer.

**Better mental model** The 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

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

Physical conclusion

Infer a field from referenced frequency or a calibrated static response, and retain intensity, blanks and directions with that inference.

## Related experiments and articles

Continue exploring

### From spin preparation to magnetic readout

How does prepared atomic orientation become an optical magnetic-field measurement?

1. [Lab **Optical Pumping and Relaxation** Prepare atomic populations and compare pumping with relaxation.](https://sandboxphysics.com/labs/optical-pumping-relaxation/)
2. [Lab **Hanle Lifetime Spectrometer** Read how an optical Hanle line depends on the excited-state lifetime; keep that lifetime distinct from ground-state relaxation.](https://sandboxphysics.com/labs/hanle-lifetime-spectrometer/)
3. [Lab **Lock-In Amplifier** Compare signed cosine and negative-sine channels with a retained reference.](https://sandboxphysics.com/labs/lock-in-amplifier/)
4. [You are here **Optically Pumped Magnetometer** Infer a resonance from counted probe light and compare probe drift with pump drift.](https://sandboxphysics.com/labs/optically-pumped-magnetometer/)

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Reading a magnetic field in the rhythm of atoms**](https://sandboxphysics.com/stories/instruments/optically-pumped-magnetometer/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)