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Sandbox Physics
Molecules, forces and ultrafast dynamics

Apparatus · Observation · Inference

Attosecond pulses: how electrons timed the shortest flashes of light

Sandbox Physics ·

How did electron spectra show that light came in bursts shorter than a femtosecond, both as a train of pulses and as a single pulse?

  1. High harmonics from a gas
  2. XUV light plus a delayed infrared field
  3. Electron energy versus delay
  4. Infer phase and duration
RABBIT measures pulse trains and streaking measures single pulses. The two record different signals and rely on different assumptions to recover the pulse.

High harmonics gave the bandwidth, but not the timing

High harmonics generated in gases supply a broad extreme-ultraviolet spectrum, the bandwidth that very short pulses need. L’Huillier’s work helped establish this source and explain how it works. Bandwidth alone does not fix the duration: relative spectral phases determine how sharply the components add within each burst. An evenly spaced harmonic comb still repeats in time when those phases change. Isolating one burst also requires control of when the harmonics are emitted and which part of the spectrum is selected.

The 2023 scientific background treats making this light and measuring it as separate achievements. The measurements came in 2001. Agostini’s group characterized a train of bursts, each roughly 250 attoseconds long; Krausz’s group characterized a single isolated pulse. A train and a single pulse have different structures in time, so one result cannot stand in for the other.

Sources: [2][4]

RABBIT: two paths to the same electron energy interfere

An electron can reach the same final energy by two routes: by absorbing a lower XUV harmonic and an infrared photon, or by absorbing the next higher odd harmonic and emitting an infrared photon. The infrared step places electrons in a sideband between the harmonic peaks. The two routes interfere, so the sideband yield oscillates as the infrared delay is scanned. Its oscillation phase carries the phase difference between the two harmonics.

That phase has two parts: the spectral phase of the XUV light and a two-photon phase contributed by the atom. A measured phase therefore cannot be read directly as the moment the source emitted light. Reconstructing the pulse train also needs the harmonic amplitudes and a stated correction or approximation for the atomic part.

Sources: [2][4][5]

Streaking: the infrared field shifts each electron by its release time

For a single XUV burst, a synchronized infrared field changes each photoelectron’s final momentum by an amount that depends on when the electron was released. Recording electron energy against delay turns that timing into a spectrogram. In their abstract, Hentschel and coauthors report a soft-X-ray pulse lasting 650 attoseconds, with an uncertainty of 150 attoseconds.

In the simplest classical picture, integrate the electric force on an electron released at the stated time and assume the infrared vector potential vanishes after the pulse. With the electric-field convention below and the elementary charge positive, the momentum shift has a minus sign. This dipole approximation neglects the magnetic force, the residual ion’s Coulomb field and scattering.

E(t)=−∂A(t)∂tpf≃p0−eA(t0),e>0\begin{aligned}\mathbf E(t)&=-\frac{\partial\mathbf A(t)}{\partial t}\\\mathbf p_f&\simeq\mathbf p_0-e\mathbf A(t_0),\qquad e>0\end{aligned}

Sources: [3][2][5]

The duration comes from a model of the measurement

Both methods obtain a duration by applying a model of the measurement to energy-versus-delay data. That model makes assumptions about the target atoms, the infrared dressing field and the retrieval method. Neither method films an electron orbit frame by frame. When comparing reported delays, differences in phase convention and atomic response matter.

Chirped-pulse amplification (CPA) supplies the intense, short driving pulse. It does not measure harmonic phases or reconstruct an attosecond pulse, so the site’s femtosecond-source Lab does not count as an attosecond measurement instrument.

Sources: [2][3][1][5]

Look at the measured trace before the reconstructed pulse

When you read a reported duration, keep the measured sideband oscillation or streaking trace beside it, and find out which atomic-phase correction or propagation approximation produced it. The linked CPA model covers only how the driving pulse is made. Measuring attosecond pulses is a separate task that it does not attempt.

Sources: [2][3]

Sources and reading notes

We read indexed passages of the Academy’s scientific background, the CEA team’s account, the Hentschel author abstract, and sections 1.2.2–1.2.3 of the Dahlström–L’Huillier–Maquet author manuscript on streaking and RABITT, including the atomic contribution to phase. The full official background PDF could not be opened. Durations quoted are the authors’ reported measurements; we did not reanalyze their data.

  1. D. Strickland, Generating High-Intensity Ultrashort Optical Pulses (2018), original CPA apparatus passage

    We read an indexed passage by the author: spectral broadening and stretching in fibre, amplification in Nd:glass and compression with gratings. The full lecture’s address returned HTTP 403.

  2. Royal Swedish Academy of Sciences, Scientific Background: Physics Prize 2023, generation and metrology sections

    We read indexed passages of the scientific background: high-harmonic generation, RABBIT pulse trains and streaking of isolated pulses. The official PDF returned HTTP 403. This document is an institutional retrospective.

  3. M. Hentschel et al., Attosecond metrology, Nature414,509–513 (2001)

    We read the author abstract, which reports 650 attoseconds with an uncertainty of 150 attoseconds. The publisher’s full article was not used.

  4. CEA attophysics team, Femtosecond–attosecond physics and chemistry: original pulse-train account

    We read the team’s own account: the 2001 RABBITT characterization of 250-attosecond bursts, and later measurements of harmonic phase and chirp.

  5. J. M. Dahlström, A. L’Huillier & A. Maquet, Introduction to attosecond time-delays in photoionization (2012), author manuscript, sections 1.2.2–1.2.3

    Read the abstract and author-manuscript sections 1.2.2–1.2.3: the instantaneous-streaking momentum sign in equation 5 and the two-photon phase in RABITT. The manuscript distinguishes measurement-induced phase from one-photon ionization delay. Other sections were not reviewed in full. Read the hosted original

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