Attosecond physics

Attosecond science mainly employs pump–probe spectroscopic methods to investigate the physical process of interest.

Due to the complexity of this field of study, it generally requires a synergistic interplay between state-of-the-art experimental setup and advanced theoretical tools to interpret the data collected from attosecond experiments.

[1] The main interests of attosecond physics are: One of the primary goals of attosecond science is to provide advanced insights into the quantum dynamics of electrons in atoms, molecules and solids with the long-term challenge of achieving real-time control of the electron motion in matter.

[5] The advent of broadband solid-state titanium-doped sapphire based (Ti:Sa) lasers (1986),[6] chirped pulse amplification (CPA)[7] (1988), spectral broadening of high-energy pulses[8] (e.g. gas-filled hollow-core fiber via self-phase modulation) (1996), mirror-dispersion-controlled technology (chirped mirrors)[9] (1994), and carrier envelop offset stabilization[10] (2000) had enabled the creation of isolated-attosecond light pulses (generated by the non-linear process of high harmonic generation in a noble gas)[11][12] (2004, 2006), which have given birth to the field of attosecond science.

This was followed by the 2023 Nobel Prize in Physics, where L'Huillier, Krausz and Pierre Agostini were rewarded “for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter.” The natural time scale of electron motion in atoms, molecules, and solids is the attosecond (1 as= 10−18 s).

10 eV, which is the typical electronic energy range in matter,[5] the characteristic time of the dynamics of any associated physical observable is approximately 400 as.

[16] To generate a traveling pulse with an ultrashort time duration, two key elements are needed: bandwidth and central wavelength of the electromagnetic wave.

[17] From Fourier analysis, the more the available spectral bandwidth of a light pulse, the shorter, potentially, is its time duration.

[18] Thus, a smaller time duration requires the use of shorter, and more energetic wavelength, even down to the soft-X-ray (SXR) region.

For this reason, standard techniques to create attosecond light pulses are based on radiation sources with broad spectral bandwidths and central wavelength located in the XUV-SXR range.

[19] The most common sources that fit these requirements are free-electron lasers (FEL) and high harmonic generation (HHG) setups.

Once an attosecond light source is available, one has to drive the pulse towards the sample of interest and, then, measure its dynamics.

W/cm2) low-frequency infrared pulse with a time duration of few to tens femtoseconds are collinearly focused on the studied sample.

[25] The subsequent challenge is to interpret the collected data and retrieve fundamental information on the hidden dynamics and quantum processes occurring in the sample.

[20][21][23] Attosecond physics typically deals with non-relativistic bounded particles and employs electromagnetic fields with a moderately high intensity (

[28] This fact allows to set up a discussion in a non-relativistic and semi-classical quantum mechanics environment for light-matter interaction.

is also known as time reversed S-matrix amplitude[32] and it gives the probability of photoionization by a generic time-varying electric field.

SFA is the starting theory for discussing both high harmonic generation and attosecond pump-probe interaction with atoms.

The main assumption made in SFA is that the free-electron dynamics is dominated by the laser field, while the Coulomb potential is regarded as a negligible perturbation.

[39] As a consequence, the final momentum distribution of a single electron in a single-level atom, with ionization potential

[41] This kind of experiments can be easily described within strong field approximation by exploiting the results of Eq.

As a simple model, consider the interaction between a single active electron in a single-level atom and two fields: an intense femtosecond infrared (IR) pulse (

Consequently, for typical experimental condition, the latter process is disregarded, and only direct ionization from the attosecond pulse is considered.

In addition to that, we can re-write the attosecond pulse as a delayed function with respect to the IR field,

describes the photoionization phenomenon of two-color interaction (XUV-IR) with a single-level atom and single active electron.

This peculiar result can be regarded as a quantum interference process between all the possible ionization paths, started by a delayed XUV attosecond pulse, with a following motion in the continuum states driven by a strong IR field.

[32] The resulting 2D photo-electron (momentum, or equivalently energy, vs delay) distribution is called streaking trace.

The most used technique is based on the frequency-resolved optical gating for a complete reconstruction of attosecond bursts (FROG-CRAB).

In other words, FROG-CRAB is based on the conversion of an attosecond pulse into an electron wave-packet that is freed in the continuum by atomic photoionization, as already described with Eq.

[41][48] The reconstruction of both the low-frequency field and the attosecond pulse from a streaking trace is typically achieved through iterative algorithms, such as: