---
title: "Zeeman Polarization Spectrometer Interactive Lab | Sandbox Physics"
description: "What does a spectral line look like in a magnetic field, viewed across and along the field?"
canonical_url: "https://sandboxphysics.com/labs/zeeman-polarization-spectrometer/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/zeeman-polarization-spectrometer/"
last_modified: "2026-10-27"
---

Quantum evidence / Light in a magnetic field

# Zeeman Polarization Spectrometer

**What does a spectral line look like in a magnetic field, viewed across and along the field?** For atoms with zero total spin, it splits into three evenly spaced frequencies. Looking across the field, you see all three, and the middle one is polarized along the field. Looking along the field, the middle one vanishes and only the two outer, circularly polarized lines remain. Their spacing gives the field strength.

Look at a spin-zero atomic line from across the magnetic field and from along it. Rotate the polarization analyzer, count photons across the spectrum and work out the field from the components that get through.

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

The Lab simulates an ideal normal Zeeman triplet based on the red cadmium singlet line. It assumes equal populations in the upper sublevels, a Gaussian spectral selector and an ideal linear analyzer. The anomalous Zeeman effect, isotope shifts, self-absorption and Fabry–Pérot ring reconstruction are not included.

Schematic geometry with enlarged gaps and parts. The colors and moving markers do not show visible light or measured trajectories. Drag to orbit.

Exposure: signal and reference counted separately

## Give the spectrum a record.

Each coordinate has a signal exposure and a separate reference: whole-line monitor. Exposure time controls Poisson noise; scan playback is accelerated.

Ready. Predict, then acquire.

Recorded points

$0$

Outer-line separation · source

$0$

Single-side shift per field

$0$

Measured spectrum in counts per second

### Which structure survives measurement?

$\Delta\nu/\mathrm{GHz}$ · $N_i/\tau_i\;(\mathrm{s^{-1}})$

Teal: source expectation. Gold: acquired rates with fitted Poisson standard deviations, once a fit exists. Purple dashes: inference from records. Gray dots: saved run. Background is included.

Click or drag to move the probe; its slider supports keyboard input. The vertical scale follows the data.

Inference with a joint Poisson likelihood

### Estimate from both exposures.

Inferred field magnitude

$\text{—}$

Inferred source rate

$\text{—}$

Deviance per degree

$\text{—}$

Zero-field alternative

$\text{—}$

$r_i=(N_i-\widehat\mu_i)/\sqrt{\widehat\mu_i}$

Gold: signal residuals. Blue: reference residuals. Known width, viewing angle, analyzer or stationary fraction, and background; unknown source rate and target field or energy. At least sixteen distinct probe positions are required. Descriptive residuals and deviance do not establish identifiability, confidence intervals or discovery significance.

### Keep the original counts.

Save a full or partial run, with its settings and seed, for as long as this page stays open.

| # | $\Delta\nu/\mathrm{GHz}$ | Signal | Whole-line monitor | $\tau/\mathrm{s}$ |
| --- | --- | --- | --- | --- |

The latest six points are shown. The CSV has every raw count, exposure, setting and unit, plus the seed. Moving the probe never changes data already taken.

Scientific scope, geometry & primary sources

The spin-zero orbital model groups nine allowed singlet transitions into three frequencies. The upper magnetic sublevels have equal populations. A linear analyzer transmits the projection of each dipole radiation pattern; transverse parallel selection leaves only the field-insensitive central line. Along the field, the central component vanishes and rotating a linear analyzer leaves equal outer components. Circular handedness is not measured here.

Physical field is scene up. A lamp sits in the gap of two bored pole pieces; the optical arm collects either across the gap or through their axial aperture. Analyzer bars rotate in the same plane used by the response. The incoming ray reaches the upstream counter face. Gaps, source, apertures and supports are schematic and enlarged.

The scan uses an ideal calibrated Gaussian spectral selector followed by a photon counter, not a simulated Fabry–Pérot image. Each channel integrates 0.875 GHz. A separate whole-line reference bypasses the spectral selector after the same analyzer. The source rate means total post-analyzer collected flux; throughput and background are assumed calibrated.

The line is inspired by the approximately 643.8 nm cadmium singlet, but no absolute wavelength or isotope centroid is inferred. Linear orbital Zeeman shifts alone are retained. No spin, isotope structure, finite angular acceptance, lamp kinetics, self-absorption or magnetic calibration uncertainty is included. The normal triplet also has a classical oscillator explanation; observing this ideal pattern alone does not establish electron spin.

Independent Poisson exposures, fixed calibrated background and stable source. No drift, dead time or calibration uncertainty. The source follows the displayed model; successful recovery validates the simulator, not the historical discovery.

[Basel / PHYWE · normal Zeeman apparatus](https://fp.physik.unibas.ch/documents/fp40_Zeeman_Effect.pdf) [NIST · CODATA constants](https://physics.nist.gov/cuu/Constants/Table/allascii.txt)

[Read the related historical evidence](https://sandboxphysics.com/stories/quantum-evidence/zeeman-lines-polarization-lorentz/) [Canal-Ray Doppler Spectrometer](https://sandboxphysics.com/labs/canal-ray-doppler-spectrometer/)

Physics tutorial

## Zeeman Polarization Spectrometer

**Background** Look at a spin-zero atomic line from across the magnetic field and from along it. Rotate the polarization analyzer, count photons across the spectrum and work out the field from the components that get through.

**Why it matters** A spectral line becomes evidence only after you measure it and know how the instrument responds to it.

Start with the essentials

- **Focus question**: What does a spectral line look like in a magnetic field, viewed across and along the field?
- **One-sentence intuition**: Keep every signal and reference count. Fit them together with one Poisson likelihood, and estimate the source rate from those same counts.

### Core mathematical model

#### Shifts of the normal Zeeman triplet

$$
\Delta\nu_q=q\,\frac{\mu_{\mathrm B}B}{h},\qquad q\in\{-1,0,1\}
$$

The two outer components move in opposite directions. The fit estimates the size of the field, not its sign, because a linear analyzer cannot tell the two circular polarizations apart.

#### Weights of the three components

$$
w_0=\sin^2\theta\cos^2\alpha,\quad w_{\pm}=\frac{\cos^2\theta\cos^2\alpha+\sin^2\alpha}{2},\quad\sum_q w_q=1
$$

The viewing angle is measured from the field. The analyzer angle is measured from the field's projection across the line of sight. When you look along the field, the analyzer angle is measured from a fixed transverse direction in the lab instead.

#### Two independent exposures

$$
N_i\sim\operatorname{Poisson}\!\left[\tau_i(Sg_i+b)\right],\qquad M_i\sim\operatorname{Poisson}\!\left[\tau_i(S+b)\right]
$$

The background rate is known in advance. The source rate and the spectral parameter are fitted together, and the uncertainty of the reference counts is included. Counts are drawn as Poisson numbers, never rounded from a Gaussian.

### Common difficulties

#### Recovering a parameter does not test the law

**Typical misconception** If the fit is good, the law built into the simulator has been independently confirmed.

**Better mental model** The simulator is given the source response in advance. Recovering the parameter shows only that this simulated measurement and fit work correctly together. The deviance and residuals describe the fit; they are not confidence intervals, significance tests or outside scientific certification.

### Run the experiment

1. 01

   #### Resolve the triplet and count

   Choose Transverse triplet, scan, then save the run.

   **What to observe:** The three source peaks turn into noisy counts in each channel, and the fit returns a field strength.

2. 02

   #### Remove the field information

   Choose Only the central line and scan again.

   **What to observe:** Photons are still counted, but the counts no longer depend on the field at all. No field estimate is reported.

3. 03

   #### Look along the field

   Choose Look along the field, then rotate the analyzer.

   **What to observe:** The central line disappears, and the two outer lines keep equal weights.

Physical conclusion

The Lab simulates an ideal normal Zeeman triplet based on the red cadmium singlet line. It assumes equal populations in the upper sublevels, a Gaussian spectral selector and an ideal linear analyzer. The anomalous Zeeman effect, isotope shifts, self-absorption and Fabry–Pérot ring reconstruction are not included.

## Related experiments and articles

Quantum evidence · Reading path

### Fields, spins and precision spectra

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

1. [Article **Why a magnetic field splits a spectral line**](https://sandboxphysics.com/stories/quantum-evidence/zeeman-lines-polarization-lorentz/)
2. [Lab **Coupled Spin Spectroscopy** See how levels and line strengths change with the field](https://sandboxphysics.com/labs/coupled-spin-spectroscopy/)

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

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