Attosecond dynamics through a Fano resonance: Monitoring the birth of a photoelectron

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Science  11 Nov 2016:
Vol. 354, Issue 6313, pp. 734-738
DOI: 10.1126/science.aah5188

Watching as helium goes topsy-turvy

Theorists have long pondered the underpinnings of the Fano resonance, a spectral feature that resembles adjacent rightside-up and upside-down peaks. An especially well-studied instance of this feature appears in the electronic spectrum of helium as a transient state undergoes delayed ionization. Two studies have now traced the dynamics of this state in real time. Gruson et al. used photoelectron spectroscopy to extract the amplitude and phase of the electron wave packet after inducing its interference with reference wave packets tuned into resonance at variable delays. Kaldun et al. used extreme ultraviolet absorption spectroscopy to probe the transient state while variably forcing ionization with a strong near-infrared field.

Science, this issue pp. 734 and 738


The dynamics of quantum systems are encoded in the amplitude and phase of wave packets. However, the rapidity of electron dynamics on the attosecond scale has precluded the complete characterization of electron wave packets in the time domain. Using spectrally resolved electron interferometry, we were able to measure the amplitude and phase of a photoelectron wave packet created through a Fano autoionizing resonance in helium. In our setup, replicas obtained by 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 resolves the buildup of the autoionizing resonance on an attosecond time scale. Our results, in excellent agreement with ab initio time-dependent calculations, raise prospects for detailed investigations of ultrafast photoemission dynamics governed by electron correlation, as well as coherent control over structured electron wave packets.

Tracking electronic dynamics on the attosecond time scale and angstrom length scale is a key to understanding and controlling the quantum mechanical underpinnings of physical and chemical transformations (1). One of the most fundamental electronic processes in this context is photoionization, the dynamics of which are fully encoded in the released electron wave packet (EWP) and the final ionic state. The development of broadband coherent sources of attosecond pulses has opened the possibility of investigating these processes with attosecond resolution. On such a short time scale, few techniques (25) are able to provide access to both spectral amplitude and phase. The spectral derivative of the phase, the group delay, is a practical quantity for describing general wave packet properties reflecting the ionization dynamics. Recently, photoemission delays have been measured in a variety of systems: noble gas atoms (68), molecules (9), and solids (10). In the gas phase, these attosecond delays give insight into the scattering of the electron in the ionic potential; in the solid state, they provide information on the transport dynamics toward the surface. However, the physical relevance of group delays is restricted to fairly unstructured wave packets.

The necessity to go beyond simple delays arises for more complex ionization dynamics when the broadband excitation encompasses continuum structures associated with, for example, autoionizing states, shape resonances, and Cooper minima (1113). These structures induce strong spectral variations of the amplitude and phase of the EWP corresponding to different time scales, ranging from the attosecond to the femtosecond domains. In general, the long-term evolution of the EWP amplitude [e.g., the lifetime of Fano autoionizing resonances (14)] can be characterized directly in the time domain (15), or in the spectral domain with the use of conventional spectroscopic techniques (16). However, the EWP phase is required for reconstruction of the full ionization dynamics. In particular, the short-term response associated with broadband excitation remains unexplored (17). It is mainly determined by the spectral phase variation over the resonance bandwidth, which has so far not been measured. An additional difficulty is that the characterization techniques often involve strong infrared probe fields that (i) strongly perturb the resonant structures (1820) so that the field-free intrinsic dynamics cannot be accessed, and (ii) require elaborate theoretical input for decoding the electron spectrograms (21).

Here, we extend attosecond photoionization spectroscopy to the full reconstruction of the time-dependent EWPs produced by coherent broadband excitation through resonant structures. To this end, we have developed a perturbative interferometric scheme enabling the direct measurement of the spectral amplitude and phase of the unperturbed resonant EWP. Interferences between the latter and a reference nonresonant EWP are achieved through two-photon replicas obtained by photoionizing the target with an extreme ultraviolet (XUV) harmonic comb combined with the mid-infrared (MIR) fundamental field. This spectrally resolved technique is easy to implement and offers straightforward access to the EWP characteristics without complex analysis or theoretical input. We apply it to the investigation of the test case of the doubly excited 2s2p autoionizing resonance of helium, for which ab initio time-dependent calculations can be performed (22, 23), thereby providing a benchmark for our experimental study.

Autoionization occurs when a system is excited in structured spectral regions where resonant states are embedded into a continuum. The system can then either directly ionize or transiently remain in the resonant bound state before ionizing. Coupling between the resonant state and continuum states of the same energy through configuration interaction leads to the well-known Fano spectral line shapes (14). Of particular interest is the autoionization decay from doubly excited states (16) that is a direct consequence of the electron-electron repulsion. Using our spectrally resolved technique, we directly access the complete ionization dynamics (including interferences at birth time) and monitor the resonance buildup on a subfemtosecond time scale—an endeavor of attosecond science (17, 24).

The concept of the method is shown in Fig. 1A. We photoionize helium with a comb of mutually coherent odd harmonics derived from an optical parametric amplifier (OPA) MIR source. The harmonic of order 63 (H63) is driven into the 2s2p resonance, at 60.15 eV from the ground state, by tuning the OPA central wavelength λOPA to 1295 nm. Because the harmonic width (400 meV) is much larger than the resonance width (Γ = 37 meV), a broad resonant EWP with complex spectral amplitude AR(E) is produced. Simultaneously, nonresonant EWPs are created by the neighboring harmonics H61 and H65 in smooth regions of the continuum; each of these can serve as a reference, denoted ANR(E), to probe the resonant EWP.

Fig. 1 Principle and resulting spectrogram of spectrally resolved attosecond electron interferometry for the complete characterization of resonant EWPs.

(A) Principle of the electron interferometry technique. Resonant AR and reference nonresonant ANR EWPs are produced by successive coherent harmonics. Replicas of these EWPs are created at the same final energy by two-photon transitions induced by a weak fundamental MIR field, where the atom absorbs a MIR photon, leading to the AR+1 EWP, or emits a MIR photon, leading to the ANR–1 EWP. The spectrally resolved interferences are measured in a time-of-flight electron spectrometer as a function of the XUV-MIR delay τ, controlled with interferometric accuracy; these interferences provide access to the spectral phase of the resonant AR EWP. (B and C) Experimental spectrogram (B) and theoretical spectrogram (C) in the 33- to 39-eV region for a 1295-nm OPA wavelength (25). H63 overlaps the 2s2p resonance of helium located 60.15 eV above the ground state (ER = 35.55 eV). Single-photon ionization by the odd harmonic orders results in main lines spaced by twice the MIR photon energy, 2ħω0 = 1.92 eV. Between these lines appear sidebands corresponding to two-photon ionization. The oscillations of the two sidebands on both sides of the resonant H63 (i.e., SB62 and SB64) encode the spectral phase of the resonant EWP. A close-up of one SB62 beating shows the structured shape of this resonant EWP and the dephasing of the oscillations of the different spectral components.

To induce interference, we use two-photon transitions to create replicas that spectrally overlap with each other. A weak fraction of the fundamental MIR pulse, of angular frequency ω0 = 2πcOPA, is superimposed on the harmonic comb with a delay τ. Its intensity (~2 × 1011 W/cm2) is sufficiently high to induce perturbative two-photon XUV-MIR transitions but is low enough to avoid transitions involving more than one MIR photon [e.g., depletion of the doubly excited state by multiphoton ionization (15), or distortion of the resonance line shape (19)]. Most important, the MIR spectral width (26 meV) is smaller than both the harmonic and resonance widths, ensuring that each EWP produced in the two-photon process is a faithful, spectrally shifted, replica of the unperturbed EWP produced in the XUV one-photon process. Because of the frequency relation between the odd-harmonic XUV comb and the fundamental MIR laser, the resonant EWP upshifted by absorption of a MIR photon, AR+1(τ, E + ħω0) ∝ AR(E) exp(iω0τ), and the reference EWP downshifted by stimulated emission of a MIR photon, ANR–1(τ, E + ħω0) ∝ ANR(E + 2ħω0) exp(–iω0τ), coherently add up in the single sideband (SB64) that lies between the lines associated with H63 and H65. Similarly, the resonant EWP downshifted by emission of a MIR photon interferes in sideband SB62 with the EWP upshifted by absorption of a MIR photon from H61. We designate E the photoelectron energy in the resonant EWP, and Embedded Image = E ± ħω0 the photoelectron energy of the resonant EWP replicas in SB64 and SB62, respectively.

The spectrum of these sidebands is thus modulated by the interference between the resonant and nonresonant replicas, depending on the XUV-MIR delay τ (25). For SB64, the spectrum is given byEmbedded Image (1)where the two contributions to the replicas’ relative phase are (i) 2ω0τ, the phase introduced by the absorption or simulated emission of the MIR photon, and (ii) the relative phase between the initial one-photon EWPs. The latter is split into Embedded Image, the phase difference between the two ionizing harmonics, and Embedded Image, the difference between the nonresonant and resonant scattering phases of the two intermediate states. In our conditions, the variations over the sideband width of both Embedded Image and Embedded Image are negligible in comparison with that of the resonant scattering phase Embedded Image (25). The latter contains information about the scattering of the photoelectron by the remaining core, including strongly correlated scattering by the other electron close to the resonance. This phase is the measurable quantity addressed by our study.

Using a high-resolution (~1.9%) magnetic-bottle spectrometer with a length of 2 m, we have access to the photoelectron spectrogram—electron yield as a function of energy E and delay τ—spectrally resolved within the harmonics and sideband widths (Fig. 1B). As a result of its large bandwidth, H63 produces a photoelectron spectrum exhibiting a double structure with a Fano-type resonant peak and a smoother peak. This shape is replicated on each of the closest resonant sidebands (SB62 and SB64). Strikingly, the components of the double structure oscillate with different phases when τ is varied, in both SB62 and SB64.

These phase variations are further evidenced by a spectrally resolved analysis: For each sampled energy within the sideband width, we perform a Fourier transform of S63±1(τ, E + ħω0) with respect to τ to extract the amplitude and phase of the component oscillating at 2ω0 (see Eq. 1 and Fig. 2). The SB62 phase shows a strong increase of ~1 rad within the resonant peak, followed by a sudden drop at the amplitude minimum (Embedded Image ~ 34.75 eV), and a rather flat behavior under the smooth peak. The SB64 phase has a very similar shape and magnitude but with an opposite sign due to opposite configuration of the resonant and reference EWPs in the interferometer. This correspondence confirms the direct imprint of the intermediate resonance on the neighboring sidebands.

Fig. 2 Resonant EWP in the spectral domain.

Upper and lower panels respectively show spectral amplitude and phase of the 2ω0 component of SB62 (left), SB64 (center), and SB66 (right) from the spectrograms in Fig. 1, B and C. The phase origin is set to 0 by removing the linear variation due to the ionizing harmonic radiation (attochirp) (30). The experimental data (purple curves) show very good agreement with the simulations (dashed black lines). The resonance position shifted by one MIR photon is indicated in gray. The measured spectral amplitudes and phases of the resonant SB62 and SB64 are easily related to the amplitude |AR(E)| and phase ηscat(E) of the resonant one-photon EWP (see Eq. 1). The main limitation comes from the current spectrometer resolution (in our conditions, a relative resolution of ~1.9% resulting in a width of ~190 meV at 10 eV) that broadens the resonant peak and its phase variations. The nonresonant SB66 exhibits a Gaussian amplitude (which mostly reflects the ionizing XUV spectral profile) and a smooth close-to-linear phase. This provides a temporal reference for the ionization dynamics.

The 2ω0 component of the resonant sidebands thus provides a good measure of the |AR(E)| exp[iηscat(E)] EWP that would result from one-photon Fourier-limited excitation. This allows a detailed study of the temporal characteristics of resonant photoemission, in particular of the electron flux into the continuum, through the direct reconstruction of this EWP in the time domain:Embedded Image (2)The temporal profile obtained from SB64 is shown in Fig. 3A. It presents a strong peak at the origin—given by the maximum of the Fourier transform of the nonresonant SB66 (25)—followed by a deep minimum around 4 fs and then a revival with a decay within ~10 fs. The presence of a fast phase jump (~2 rad within ~2 fs) at the position of the minimum indicates that it results from a destructive interference between two wave packet components, the origin of which is detailed below.

Fig. 3 Resonant EWP in the time domain and time-resolved reconstruction of the resonance buildup.

(A) Temporal profile of the resonant EWP obtained by Fourier transform of the SB64 data (i) from the experimental spectrogram (solid purple curve) and corresponding temporal phase (dashed purple curve), and (ii) from the simulated spectrogram, taking into account (dotted orange curve), or not (dot-dashed black curve), the finite spectrometer resolution. The latter fully coincides with the one-photon resonant EWP profile from a direct analytical calculation (solid gray curve) (25), thereby demonstrating the validity of our interferometric technique. (B) Illustration of the formation dynamics of the resonant spectrum resulting from interference between the two paths in the Fano autoionization model. (C) Reconstruction of the time-resolved buildup of the resonant spectrum using the time-energy analysis introduced in Eq. 5. The photoelectron spectrum is plotted as a function of the upper temporal limit (accumulation time tacc) used for the inverse Fourier transform. The dashed gray curve, solid blue curve, and solid red curve indicate accumulation times of 0, 3, and 20 fs, respectively. (D) Lineouts of (C) every 1 fs. This figure evidences first the growth of the direct path until a maximum is reached at ~3 fs (blue curves), and then the increasing spectral interference with the resonant path that finally results in the Fano line shape (red curves). At 35.6 eV, an isosbestic-like point is crossed by all curves from 3 fs onward (black circle), evidencing a position in the final line shape where only the direct path contributes.

To benchmark the measured data, we theoretically investigated the multicolor XUV + MIR ionization of He in the vicinity of the 2s2p resonance. Fully correlated ab initio time-dependent calculations (22) were used to validate an analytical model of the two-photon transitions accounting for the actual pulses’ bandwidths (23). The simulated photoelectron spectrogram, taking into account the spectrometer resolution, remarkably reproduces the structured shape of the resonant sidebands as well as the dephasing between their two components (Fig. 1C). The analysis of the 2ω0 oscillations of SB62 and SB64 gives spectral phase variations in excellent agreement with the experimental data (Fig. 2). The temporal profile Embedded Image obtained by Fourier transform (Fig. 3) is also well reproduced, with a smaller revival but a similar decay time of ~10 fs. This reduced effective lifetime is a direct consequence of the finite spectrometer resolution. When the latter is assumed infinite, the time profile has the same behavior at short times but a longer decay, corresponding to the 17-fs lifetime of the resonance. Analytical calculations show that in our conditions, the reconstructed EWP does mirror the one-photon resonant EWP (25). These findings confirm that, except for a faster decay of the long-term tail due to our current electron spectrometer resolution, the essential physics of the early time frame of EWP creation is directly accessed from purely experimental data.

To further highlight the insight provided by this experimental technique, we undertook an in-depth analysis of the measured EWP characteristics in terms of Fano’s formalism for autoionization (14). Resonant ionization can be described as the interference between two distinct paths: (i) the direct transition to the continuum, and (ii) the resonant transition through the doubly excited state that eventually decays in the continuum through configuration interaction within the resonance lifetime (Fig. 3B). The normalized total transition amplitude can then be written as the coherent sum of two contributions, a constant background term and a Breit-Wigner amplitude for the resonance:Embedded Image (3)where ε = 2(EER)/Γ is the reduced energy detuning from the resonance at energy ER, in units of its half width Γ/2. The Fano parameter q [–2.77 for the He(2s2p) resonance (16)] measures the relative weight of the two paths. Their interference leads to the well-known asymmetric Fano line shape |R(E)|2 and to the resonant scattering phase: ηscat(E) = arg R(E) = atan(ε) + π/2 – πΘ(ε + q), where Θ is the Heaviside function. This phase is experimentally accessed here (Fig. 2).

The spectral amplitude of an EWP created by Gaussian harmonic excitation H(E) is given by R(E)H(E). Its temporal counterpart is Embedded Image, where Embedded Image and Embedded Image are Fourier transforms of the spectral amplitudes, in particularEmbedded Image (4)(24). The temporal profile Embedded Image thus decomposes into a Gaussian nonresonant term and a resonant contribution, like our experimental data (Fig. 3A). The destructive temporal interference between the two terms leads to the amplitude minimum and phase jump identified around t = 4 fs.

To illustrate how the interference between the two paths governs the formation of the resonance line shape, Wickenhauser et al. (17) introduced a time-frequency analysis based on the limited inverse Fourier transform:Embedded Image (5)which shows how the spectrum builds up until accumulation time tacc. The result of this transform applied to the experimental EWP in Fig. 3A is shown in Fig. 3, C and D. The chronology of the resonance formation can be nicely interpreted within Fano’s formalism. In a first stage until ~3 fs, a close-to-Gaussian spectrum reflecting the ionizing harmonic spectral shape emerges: The direct path to the continuum dominates. Then the resonant path starts contributing as the populated doubly excited state decays in the continuum: Interferences coherently build up until ~20 fs, consistent with the temporal profile in Fig. 3A, to eventually converge toward the asymmetric measured spectrum. The resonance growth can thus be decomposed in two nearly consecutive steps governed by fairly different time scales.

The buildup of the resonant profile reveals the presence of a notable point around E = 35.6 eV where, as soon as the direct ionization is completed, the spectrum barely changes with tacc any longer. This can be explained by splitting the |R(E)|2 spectrum from Eq. 3 into three terms:Embedded Image (6)(26). At this isosbestic-like point—that is, for ε = [(1/q) – q]/2—the bound (second term) and coupling (third term) contributions ultimately cancel each other, leaving only the direct continuum contribution (first term). This point thus gives a useful landmark in the resonant line shape (e.g., for cross section calibration or reference purposes).

Spectrally resolved electron interferometry thus provides insight into the ultrafast strongly correlated multielectron dynamics underlying autoionization decay. Given the generality and wide applicability of the Fano formalism [see, e.g., (26)], we anticipate that our approach, combined with progress in attosecond pulse production and particle detection (e.g., access to photoelectron angular distributions), will open prospects for studies of complex photoemission dynamics close to resonances and, more generally, structured EWP dynamics in a variety of systems, from molecules (2729) and nanostructures (26) to surfaces (10). Furthermore, the well-defined amplitude and phase distortions induced by the resonance offer a means for shaping the broadband EWP, bringing opportunities for coherent control in the attosecond regime.

Supplementary Materials

Supplementary Text

Figs. S1 to S7

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References (3143)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: We thank S. Weber for crucial contributions to the PLFA attosecond beamline; D. Cubaynes, M. Meyer, F. Penent, and J. Palaudoux for setup and testing of the electron spectrometer; and O. Smirnova for fruitful discussions. Supported by European Union grant H2020-MSCA-ITN-MEDEA-641789, Agence Nationale de la Recherche grants ANR-15-CE30-0001-01-CIMBAAD, and ANR11-EQPX0005-ATTOLAB, European Research Council advanced grant XCHEM 290853, European COST Action grant XLIC CM1204, and MINECO Project grant FIS2013-42002-R. We acknowledge allocation of computer time from CCC-UAM and Mare Nostrum BSC.
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