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.

Instrument setup

Time the light with electrons

01Light source

Five calibrated harmonics enter the timing measurement.

Driver wavelength

\lambda/\mathrm{nm}

800

Source harmonic phase curvature

\beta/\mathrm{rad}

0.18

Calibration, resolution and counting

The atomic phase is a declared input. Energy resolution and exposure set the line width and counting noise.

Declared atomic-phase slope

\theta_1/\mathrm{rad}

0.25

Electron energy response standard deviation

\sigma_E/\mathrm{eV}

0.14

Exposure per delay

C

700

Changing the setup keeps the previous records and marks them as a comparison. The probe beside the 3D bench only changes the view of the instrument.

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.

01Set the instrument
02Record the scan
03Infer 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.

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.

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 misconceptionThe measured phase is entirely the light pulse’s phase.

Better mental modelThe 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

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.
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.
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