---
title: "Attosecond RABBIT Metrology Interactive Lab | Sandbox Physics"
description: "How can electron spectra reveal the duration of an attosecond pulse train? The delay-dependent electron sidebands reveal phase differences between neighboring harmonics. Combine those phases with calibrated harmonic strengths to recover the pulse train; the atom’s contribution must be accounted for."
canonical_url: "https://sandboxphysics.com/labs/attosecond-rabbitt-metrology/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/attosecond-rabbitt-metrology/"
last_modified: "2026-10-23"
---

B-X3 · Time from electron spectra

# Attosecond RABBIT Metrology

**How can electron spectra reveal the duration of an attosecond pulse train?** The delay-dependent electron sidebands reveal phase differences between neighboring harmonics. Combine those phases with calibrated harmonic strengths to recover the pulse train; the atom’s contribution must be accounted for.

Scan the delay between ultraviolet harmonics and an infrared probe. Fit the sidebands in the recorded electron counts, correct a declared atomic phase and reconstruct the light pulses.

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

Five stationary odd harmonics and a weak infrared field ionize a schematic gas target through two perturbative paths. Harmonic amplitudes, wavelength, energy calibration and delay are known. Gaussian energy resolution and Poisson counting are included. The atomic phase is a declared teaching input, not a calculated argon response. Phase retrieval uses the recorded sideband counts. It cannot recover the absolute carrier phase or time origin. Source phases are restricted to avoid adjacent phase ambiguity. The reconstruction describes a periodic train, not an isolated streaking measurement. High-harmonic generation, resonances, Coulomb propagation, orbital-channel overlap, pulse-to-pulse changes and detector dead time are omitted. Apparatus dimensions are schematic. Delay-carriage travel is enlarged eighty thousand times. The cutaway analyzer shows an illustrative transport path; electric fields and electron trajectories are not solved.

Move the infrared delay carriage$\tau/\mathrm{fs}$ $0$

Drag the teal carriage or move the delay below. Both infrared passes lengthen together.

Physical mirror travel

$\Delta x=0.000\,\mu\mathrm m$

Probe delay

$\tau=0.00\,\mathrm{fs}$

Carriage travel is magnified eighty thousand times; particle motion is shown in slow motion.

Apparatus scale and particle motion

The carriage travel is magnified eighty thousand times. Light and electron markers move slowly to show the route; they are not individual recorded events. The analyzer is shown cut open.

Measurement sequence

## Scan the delay. Recover the pulse.

The carriage advances through sixty-four delays. Every setting adds an electron energy spectrum to the same acquisition.

1. 01 Set the instrument
2. 02 Record the scan
3. 03 Infer from counts

Ready. Choose a setup, then start the scan.

Start a scan to record counts. The spectrum will appear here as measurements arrive.

Recorded counts

### Electron energy against delay

No acquisition yet

$\tau/\mathrm{fs},\quad E_e/\mathrm{eV}$

Click the image to move the delay probe. Color shows square-root counts; the CSV retains linear counts.

Estimated from the stored scan

### The recovered pulse

Main-peak intensity FWHM

$\text{—}$

Weakest sideband signal to counting noise

$\text{—}$

Fit residual RMS

$\text{—}$

A result appears after acquisition and analysis.

Test the measurement model

### Each sideband carries a phase

$\tau/\mathrm{fs},\quad N_{\rm SB}$

Choose a sideband. Dots are sums from its recorded energy window; the curve fits those sums.

From relative phase to time

### Reconstruct one period of the train

Apply the declared atomic-phase correction to these same counts

$t/\mathrm{fs},\quad I/I_{\max}$

Teal: reconstruction from fitted phases and calibrated amplitudes. Gold dashed: separate source reference. Satellites can remain outside the main peak.

Recovered adjacent phase differences

$S_{12}$

$\text{—}$

$S_{14}$

$\text{—}$

$S_{16}$

$\text{—}$

$S_{18}$

$\text{—}$

Read the original experiment

[Historical evidence and the limits of this model](https://sandboxphysics.com/stories/probe-evidence/attosecond-pulses-and-metrology/) [Paul and colleagues, 2001](https://ir.amolf.nl/pub/1223/3763.pdf) [Atomic phase, tutorial Eq. 6](https://arxiv.org/html/1205.6624v2)

## Read the experimental evidence

The simulation uses the assumptions stated above. Read how the historical apparatus measured the effect, what its records supported, and where the interpretation was limited.

[Attosecond pulses and their measurement](https://sandboxphysics.com/stories/probe-evidence/attosecond-pulses-and-metrology/) [All six reading paths](https://sandboxphysics.com/stories/probe-evidence/)

Physics tutorial

## Attosecond RABBIT Metrology

**Background** Scan the delay between ultraviolet harmonics and an infrared probe. Fit the sidebands in the recorded electron counts, correct a declared atomic phase and reconstruct the light pulses.

**Why it matters** A broad spectrum can produce pulses of different duration. Measuring the relative phase tells us how its frequencies combine in time.

Start with the essentials

- **Focus question**: How can electron spectra reveal the duration of an attosecond pulse train?
- **One-sentence intuition**: The timing comes from the phase of a measured electron oscillation and a model of the atom.

### Core mathematical model

#### Two paths to the same sideband

$$
S_j(\tau)=A_j+B_j\cos[2\omega\tau-\Delta\phi_j-\theta_j]
$$

The neighboring-harmonic phase difference and the atomic phase both shift the twice-infrared oscillation. Positive delay means that the infrared probe arrives later.

#### Reconstruct from the fitted phases

$$
I(t)=\left|\sum_j a_j e^{-iq_j\omega t+i\widehat\phi_j}\right|^2
$$

The amplitudes are known calibration inputs. Relative phases are accumulated from the fitted sidebands after the chosen atomic correction. The absolute field phase is arbitrary.

### Common difficulties

#### A reconstructed result depends on the measurement model

**Typical misconception** The measured phase is entirely the light pulse’s phase.

**Better mental model** The atom adds a phase to the two-path signal. The correction here is a stated external input; real atomic calculations require more physics.

### Run the experiment

1. 01

   #### Record the sidebands

   Choose Phase-locked train, acquire and analyze the counts.

   **What to observe:** The energy–delay image contains oscillating sidebands. The fitted phases produce a short recurring burst.

2. 02

   #### Keep the same data, change the correction

   Choose Atomic-phase error, acquire and analyze, then switch on the atomic correction.

   **What to observe:** The count image is unchanged. The recovered phase curvature and pulse width change.

3. 03

   #### Lower the counts

   Choose Few counts and compare repeated acquisitions.

   **What to observe:** Shot noise changes the fitted phase. The duration is withheld when the oscillation is too weak.

Physical conclusion

Five stationary odd harmonics and a weak infrared field ionize a schematic gas target through two perturbative paths. Harmonic amplitudes, wavelength, energy calibration and delay are known. Gaussian energy resolution and Poisson counting are included. The atomic phase is a declared teaching input, not a calculated argon response. Phase retrieval uses the recorded sideband counts. It cannot recover the absolute carrier phase or time origin. Source phases are restricted to avoid adjacent phase ambiguity. The reconstruction describes a periodic train, not an isolated streaking measurement. High-harmonic generation, resonances, Coulomb propagation, orbital-channel overlap, pulse-to-pulse changes and detector dead time are omitted. Apparatus dimensions are schematic. Delay-carriage travel is enlarged eighty thousand times. The cutaway analyzer shows an illustrative transport path; electric fields and electron trajectories are not solved.

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

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