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.

Electrons reveal the pulse

Infrared delay

\tau/\mathrm{fs}

0

Pulse chirp

\beta/\mathrm{rad}

0.18

Drag the carriage: the electron count oscillates with delay.

Simulated preview

Calibration and counting

Driver wavelength

\lambda/\mathrm{nm}

800

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

Atomic phase is an external input. Resolution and exposure set spectral broadening and Poisson noise.

Model assumptions

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.

Carriage travel enlarged 80,000 times; pulse envelopes enlarged; transport slowed.

Geometry and visual scales

\Delta x=0\,\mu\mathrm m

\tau=0\,\mathrm{fs}

The XUV glyph length shows the generating main-peak FWHM at an enlarged spatial scale. Its source phase is a separate reference; reconstruction uses stored electron counts. Particle density and receiving-face glow scale with one stored sideband window. No electron-field trajectory or HHG propagation is solved.

Capture a new scan or choose a demo.

Electron counts across the delay scan

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

Pink cursor: delay. Color: square-root counts.

Inspect the fit and calibration

Sideband interference

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

Subtract the declared atomic phase from the same counts

S_{12}

\text{—}

S_{14}

\text{—}

S_{16}

\text{—}

S_{18}

\text{—}

Amplitudes and atomic phase are external calibrations. Sideband phases are fitted from stored counts; no credible width is reported when the signal is insufficient.

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

Attosecond RABBIT Metrology

Electron counts across the delay scan

The retrieved pulse train

Sideband interference