Posts Tagged ‘Fano resonance’

Spectroscopy has taught us how the very precise measurement of resonance lineshapes gives insight into the structure of matter. However, as a time-integrated measurement, the spectral lines give only indirect information on the underlying electronic dynamics. The resonance width can be related to the timescale of the electronic excitation and relaxation, but, in the general case, this is not enough for accessing the details of the full dynamics that have to be recovered from advanced modeling. A typical case is the one of autoionizing resonances, where the system (atom, molecule, nanostructure) can be ionized either directly to the continuum or be trapped in a very excited state for a very short time (femtosecond) before reaching the continuum. The interference between the two channels results in an asymmetric lineshape, called Fano profile after the Italian theoretician Ugo Fano who first modeled this process. While the Fano profile has been extremely successful in analyzing the absorption lines measured in a wide variety of systems, the details on how the process unwraps in time have remained elusive, the ultrashort timescale at stake precluding direct time-domain investigations.

In the November 11 issue of Science magazine, two articles tackle the problem of watching the buildup of the helium 2s2p Fano resonance from two different perspectives: from the ‘inside’ and from the ‘outside’.

In the article entitled “Observing the ultrafast buildup of a Fano resonance in the time domain” (DOI: 10.1126/science.aah6972), experimental physicists from the MPI for Nuclear Physics (MPIK, Heidelberg), together with theoretical physicists at the Vienna University of Technology and the Kansas State University look at the autoionizing process from ‘inside’ the atom by measuring the time-dependent dipole response in transient absorption spectroscopy. The dipole response being determined by the electron dynamics close to the nucleus, it provides a detailed picture of what takes place ‘inside’ the atom undergoing autoionization. In this work, short bursts of XUV light around 60.15 eV trigger the dynamic buildup of the Fano resonance by inducing an oscillating dipole moment, which in turn gives rise to the optical dipole response of the transition. A time-delayed ultrashort infrared pulse is then used to strong-field ionize the system, interrupting the autoionization process. The measured time-gated dipole response shows how the absorption lineshape evolves from an initially broad distribution to the characteristically ‘narrow’ converged Fano profile.

In the article “Attosecond dynamics through a Fano resonance: Monitoring the birth of a photoelectron” (DOI: 10.1126/science.aah5188), another team composed of experimental physicists from the CEA-CNRS-Université Paris-Saclay (CEA-Saclay) and theoretical chemists and physicists at the Université Pierre et Marie Curie (UPMC-Paris) and Universidad Autónoma de Madrid look at the autoionizing process from ‘outside’ the atom by measuring the time-dependent outgoing wavepacket, i.e. by probing the photoelectron itself. Using spectrally resolved electron interferometry, they could measure the spectral amplitude and phase of the resonant wave packet. In this scheme, replicas obtained by perturbative two-photon transitions interfere with reference wave packets that are formed through smooth continua, allowing the full temporal reconstruction, purely from experimental data, of the resonant wave packet released in the continuum. In turn, this allows resolving the ultrafast buildup of the autoionizing resonance, revealing the decomposition of the process in two nearly consecutive steps governed by fairly different time scales: during the first 3 fs, the direct ionization channel dominates; then, the resonant path starts contributing as the doubly excited state decays in the continuum, resulting in interferences between the two channels that ultimately shape the celebrated Fano profile.

These two complementary studies illustrate the large potential of the diverse techniques developed in attosecond spectroscopy: detection of photons or electrons, time-domain versus frequency-domain measurements, strong-field vs. perturbative regime. They open multiple opportunities for studying ultrafast strongly correlated dynamics in a variety of systems, from molecules and nanostructures to surfaces, and controlling matter changes at a most fundamental level.

(left) Absorption spectra measured for a series of XUV-IR delays from 6 to 32 fs (from DOI: 10.1126/science.aah6972).
(right) Experimentally-retrieved photoelectron spectrum for accumulation times from -10 to 20 fs (step=1fs) (from DOI: 10.1126/science.aah5188)

Richard Taieb, UPMC (
Thomas Pfeifer (

Ionizing radiation can bring an atom to a super-excited state that survives for an infinitesimal time before emitting one electron. Using advanced attosecond interferometric techniques, XLIC researchers from Lund, Madrid, Paris, and Stockholm have now resolved the collapse of such state in time, finally confirming a theoretical prediction formalized more than 50 years ago that has its roots at the very beginning of the quantum revolution.

When irradiated with light with sufficiently high frequency, such as extreme ultraviolet rays or x rays, matter emits electrons; this is the celebrated photoelectric effect. To explain this effect, in 1905 Einstein suggested that light was composed of photons, small packets of energy that provide individual electrons with enough momentum to escape the Coulomb attraction of atomic nuclei. Some twenty years later, quantum theory finally provided the theoretical framework necessary to formalize Einstein’s intuition: matter does exchange energy by quanta, and, in the simplest scenario, the absorption of an ionizing photon is accompanied by the instantaneous emission of an electron wave packet.

In 1933, H. Beutler [Z. Physik 86, 495], an experimental physicist, showed that things were not as simple after all. He found that the absorption spectra of rare-gas atoms above the ionization threshold exhibit wide peaks with anomalously asymmetric profiles. These peaks indicated that the atom, instead of being instantaneously ionized, could be temporarily excited to some unstable state, hence the finite width. The meaning of the peak asymmetry, however, remained obscure. The following year, Enrico Fermi, then a professor in Rome, assigned this puzzle to Ugo Fano, a 22 years old post-doctoral collaborator, who published the provisional results of his investigations in 1935 in an Italian journal. According to Fano, the asymmetry of photoelectron absorption peaks arise from the interplay between the direct-ionization wave front, predicted since the beginning, and the trailing emission from the collapsing excited atom. Due to the dispersive character of electron waves (more energetic electrons move faster than less energetic ones), the latter component catches up with the direct wave front, carving a trough where the two waves interfere destructively. It is this interference that skews the spectrum of the electrons from the decaying atom, which would otherwise be a perfectly symmetric Lorentzian peak.

Fano had to interrupt his studies of atomic photoionization due to the precipitating historical conditions that eventually lead to the outbreak of WWII.  For more than 25 years, his 1935 paper, which was written in Italian, was all but forgotten. In 1961, Fano managed to resume his studies, publishing a second more refined English version of his work which soon became one of the most cited physics papers of all times. Since then, the characteristic asymmetric photoelectron energy distribution predicted by Fano’s theory has been confirmed for countless systems. One inherent aspect of the phenomenology modeled by Fano, however, that is how the direct and resonant wave packets come together in time to give rise to the final spectral asymmetry, had eluded any direct experimental confirmation for all this time.

In a paper published on February 18th in Nature Communication, researches from Lund University, Universidad Autónoma de Madrid (UAM), Université Pierre et Marie Curie in Paris, and Stockholm University have announced that they have finally closed this long-standing gap. Using a novel attosecond interferometric laser technique developed in Lund by the experimental group of Professor Anne L’Huillier, the authors were able to compare in detail the structured wave front generated by the resonant ionization of the argon atom with the simpler direct-ionization wave obtained at energies where no metastable state is excited. Their finding closely matches the prediction of the Fano model, which researchers from UAM have extended to the multiphoton regime entailed in the experiment. This finding, which is the first “observation” of the collapse of an autoionizing atomic state, opens the way to the detailed study of the ultrafast photoelectron dynamics, which plays a fundamental role in many processes triggered by energetic light in matter, from radiation damage of biological tissues to charge emission in photoelectric cells.

Spectral phase measurement of a Fano resonance using tunable attosecond pulses
M. Kotur, D. Guénot, A. Jiménez-Galán, D. Kroon, E.W. Larsen, M. Louisy, S. Bengtsson, M. Miranda, J. Mauritsson, C.L. Arnold, S.E. Canton, M. Gisselbrecht, T. Carette, J.M. Dahlström, E. Lindroth, A. Maquet, L. Argenti, F. Martín & A. L’Huillier
Nature Communications, 7, 10566. 18 de febrero de 2016.
DOI: 10.1038/ncomms10566