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Self-Probing of Molecules with High Harmonic Generation

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Self-Probing of Molecules with High Harmonic Generation PhD TUTORIAL Self-probing of Molecules with High Harmonic Generation S Haessler,1, ∗ J Caillat,2 and P Sali`eres3 1Photonics Institute, Vienna University of Technology, Gußhausstraße 27/387, A-1040 Vienna, Austria 2UPMC, Universit´eParis 06, CNRS, UMR 7614, LCPMR, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France 3CEA-Saclay, IRAMIS, Service des Photons, Atomes et Mol´ecules,91191 Gif-sur-Yvette, France This tutorial presents the most important aspects of the molecular self-probing paradigm, which views the process of high harmonic generation as \a molecule being probed by one of its own electrons". Since the properties of the electron wavepacket acting as a probe allow a combination of attosecond and Angstr¨omresolutions˚ in measurements, this idea bears great potential for the observation, and possibly control, of ultrafast quantum dynamics in molecules at the electronic level. Theoretical as well as experimental methods and concepts at the basis of self-probing measurements are introduced. Many of these are discussed on the example of molecular orbital tomography. I. INTRODUCTION 1. Combining attosecond and Angstr¨omresolutions˚ The measurement of structural changes of matter as it undergoes processes important to physics, chemistry and biology has always been one of the prime goals of experimentalists. While in the 19th century questions like \How do cats manage to always land on their feet?" were answered [1], current technology allows to address FIG. 1. Wavelength associated with an electron (a) and a (sub-)femtosecond and Angstr¨omscales,˚ i.e. the natu- photon (b) as function of the energy. Due to their different ral scales of electrons at the atomic/molecular level (1 dispersion relation, electrons are suitable to probe Angstr¨om atomic unit of time ≈ 24 as = 24×10−18 s, 1 atomic unit structures at much lower energies than photons. of length ≈ 0.53 A=˚ 5:3 × 10−11 m). A very instructive overview of various methods cur- rently developed to achieve such extreme resolutions can found in [6]. Each of these possible \third steps" de- be found in [2]. One of these emerged during the last mands its specific theoretical modelling. decade as a by-product of efforts to generate light pulses For this tutorial, we choose to delve into only one of attosecond duration [3, 4] and is currently attracting particular outcome of inelastic electron-ion scattering; tremendous attention: the self-probing of molecules by namely the recombination of the electron with the hole it their own electrons. had left behind. As a result of recombination, the kinetic This idea is inherent to the three-step recollision model energy of the recolliding electron plus the binding energy [5] ubiquitous in strong-field physics, the field concerned are released through the emission of a photon, typically with the highly non-linear response of matter to opti- in the extreme-ultraviolet (XUV, 10{120 eV or 0.37{4.4 cal electric fields of similar strength to atomic/molecular atomic units (a.u.)) or even soft x-ray (120{1200 eV or binding fields: (i) The strong laser field tears a valence 4.4{44 a.u.) spectral range. This strong-field process electron away from the molecule through tunnel ioniza- is the so called high harmonic generation (HHG), dis- tion. (ii) The \freed" electron is accelerated in the laser covered simultaneously in Saclay [7] and Chicago [8] in field, which soon reverses its sign to toss the electron 1987. back. (iii) It may now happen that the laser driven elec- In the self-probing paradigm, the recolliding electron tron recollides with its parent ion and scatters in different takes the role of a probe pulse and the emitted photons arXiv:2103.16228v1 [physics.atom-ph] 30 Mar 2021 ways, such as inelastic scattering leading to, e.g., core ex- that of the signal carrying information on the molecule citation or double ionization; or simply elastic scattering to the detector. What makes this scheme particularly of the electron. The idea of self-probing is now noth- attractive is that this probe pulse turns out to have a set ing more than considering the electron-ion scattering as of beautiful properties found nowhere else in this combi- a probe of the molecule. An excellent overview of self- nation: probing based on different scattering mechanisms can be (i) The electron energies,pE, correspond to de-Broglie- wavelengths of λe = 2π= 2E (atomic units [9] will be used throughout the tutorial) in the range of few Angstr¨omsor˚ even sub-Angstr¨om.˚ Obtaining the same ∗ [email protected] wavelengths with photons, for which λ = 2πc=E, where c 2 is the vacuum light velocity, requires several keV energy, still open. We will not fail to mention here the most im- i.e. hard x-rays! Such x-rays are not only hard to make portant \construction sites" of the theories behind self- and control, but also primarily interact with electronic probing; a more involved introduction into this vivid de- core-states rather than the valence shell, relevant for dy- bate is attempted in [25]. We write this tutorial because namics in chemical and biological systems. A comparison we believe that a pedagogical overview of the ideas and of the wavelengths of photons and electrons is shown in concepts behind self-probing can help many researchers figure 1. with different backgrounds and different levels of experi- (ii) The whole HHG three-step process of tearing the ence, who share the common goal of dynamic imaging at electron away, accelerating it and finally making it recol- the (sub-)femtosecond and Angstr¨omscales,˚ understand lide and recombine happens in only a fraction of a driv- both the great potential and challenges of self-probing, ing laser field cycle; e.g. in less than 2.7 fs with the and hopefully discover synergies and new opportunities. commonly used 800-nm lasers. The total duration of the electron probe pulse is only ∼ 1 fs long [10]. Pushing this idea further and splitting the electron into narrow spec- 2. A bit of history tral components (quantum-mechanically, it is of course a wave packet), one can make use of its intrinsic chirp and In this section, instead of narrating the detailed devel- devise the chirp-encoded recollision scheme allowing for opment of the field over the last decade, we would just ∼ 0:1 fs temporal resolution [11{15] (cf. section III A 2). like to highlight some works we consider to be seminal To date, not even gigantic x-ray free-electron lasers such milestones for the interpretation and exploitation of high as LCLS in Stanford can provide x-ray pulses with such harmonics generated in molecules. short durations. In 2000, the Imperial college group of Jon Maran- (iii) The HHG process is driven by the laser field in gos initiated the studies of HHG in aligned molecules a fully coherent way, i.e. it happens in a macroscopic and announced that it could become a tool for studying number of molecules in the laser focus in a perfectly syn- molecular dynamics [26{29]. Shortly after, Manfred Lein chronized way, leading to a \macroscopic" light signal achieved a theoretical breakthrough when he described from a single-molecule effect—a very pleasant situation + numerical results obtained for H2 molecules with a very for experimentalists. simple analytical model, demonstrating that destructive In total, we have a probe electron wave packet (EWP) interference between the recolliding EWP and the elec- composed of wavelengths of typical molecular dimensions tron bound-state wavefunction during the recombination (∼ 1 A)˚ and with a duration similar to intra-molecular step of HHG leaves a clear signature in the harmonic electron dynamics (∼ 1 fs or less) or very rapid nuclear emission [30, 31]. dynamics, e.g. of protons. This clearly holds promise Simultaneously, the Paul Corkum group at NRC Ot- for directly time-resolving such dynamics and proba- tawa was the first to explicitly formulate the self-probing bly even for ultrafast imaging of electrons in molecules. paradigm, in the context of non-sequential double ion- \Imaging" means obtaining structural information of any ization of H2 [10]. In 2004, based on the picture of the kind|what kind, depends very strongly on the underly- electron-hole recombination in HHG as an interference ing theoretical model. between a probe EWP and the bound state, they pushed Tracking \electrons at work" in molecules has been a the idea of molecular imaging by self-probing to the ex- dream of physicists for a long time because this could treme, proposing a tomographic analysis to reconstruct tackle fundamental questions such as: When exactly is the electron bound-state wavefunction [32]. Although in the Born-Oppenheimer approximation valid and when this work, a static wavefunction had been reconstructed, does it break down [16{19]? How does the correlated the potential of ultra-fast|possibly attosecond|time re- electron cloud re-arrange after a fast perturbation and solved imaging of electrons bound in molecules was ev- how long does it take? How does this influence the sub- ident. This certainly constituted a conceptual break- sequent slower nuclear motion? Could we control and through, although based on controversial assumptions, drive the electron re-arrangement? When and how do and initiated a great number of studies by both theoreti- correlations and couplings gain importance in molecular cians and experimentalists. dynamics? Of particular interest here will be the mi- In the following years, a lot of data was produced gration of the electron-hole after sudden ionization of a around the world: the intensity of harmonics generated molecule by an attosecond light pulse or via tunnelling in aligned molecules was shown in Italy and Japan to ex- in a strong infrared field [20{23], since the first experi- hibit spectral minima [33{35].
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