Experiencia previa: practica educativa del periodo 2018 – 1

Figure 3.6: Amplitude of the asymmetry A0(W, θ) in the emission of: (a) D+ ions from the dissociative ionization of D2 and (b) H+ fragments from the dissociative ionization of HD as a function of the emission angleθ and kinetic energy W. Fig. 3.6a is adapted from [11].

3.4

Optimal pulse duration for maximal control of

electron localization

3.4.1

Asymmetry amplitude vs. pulse duration

The degree of CEP-control of the electron localization in the dissociative ionization of molecular hydrogen has been explored as a function of the laser pulse duration [10, 11]. Fig. 3.7 shows the result of that study and demonstrates that the asymmetry amplitude depends on the pulse duration. It was found that the asymmetry modulation depth (twice the asymmetry amplitude) decays exponentially from approximately 45% for 5 fs laser pulses towards 1% for pulse durations more than 9 fs [10, 11]. This finding was theoretically supported in [34, 68, 85] and can be explained by the number of peaks of the electric field contributing to ionization. The electron localization is determined by complex coupled electron-nuclear dynamics initiated by ionization by the most pronounced peaks of the laser field. Ionization at different half-cycles can lead to different final electron localization [34, 68]. As longer pulses include multiple contributing ionizations the asymmetry amplitude is smaller for longer pulses. Few-cycle pulses appear therefore a significant prerequisite for the electron localization control that has been achieved.

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Figure 3.7: Experimental asymmetry modulation depth in the emission of D+ ions between 3 and 8 eV from dissociation of D₂ vs. the laser pulse duration [11]. Individual data points correspond to single measurements within the intensity range of (1.2±0.4)×1014W cm−2. The solid blue line is an exponential decay fit of the data points.

Figure 3.8: Asymmetry of D+ ion emission from D2 as a function of ion energy and

ϕtwo−color being a phase between 800 nm and 400 nm pulses from Ref. [73]. The asymmetry

is obtained similar to Eq. 3.11 taking into account the number of ions integrated over an angle of 30◦ along the polarization axis. The ion spectrum (left panel) is shown in a logarithmic scale.

3.5 Asymmetric dissociation of molecular hydrogen in a two-color, attosecond

XUV–femtosecond near-IR field 29

3.4.2

Asymmetric dissociation of D

in a two-color femtosecond

laser field

Controlling electron motion employing subcycle field waveform control has been shown above to be feasible with CEP-controlled few-cycle waveforms. The duration of such a pulse, with a force controlled via ϕCEP, varying on sub-femtosecond scale is critical, as

shown in Fig. 3.7. The subcycle control of electric field waveforms can also be achieved by waveform synthesis [5, 86]. A recent example of applying a simple waveform synthesis in the femtosecond domain to the control of the dissociative ionization of D2 demonstrates that a similar, although not identical control can be achieved with much longer femtosecond laser pulses [73]. The asymmetric dissociation of D2 can be tailored with the relative phase

ϕtwo−color of a two-color laser field E(t) = E1(t)cos(ωt) +E2(t)cos(2ωt+ϕtwo−color) with

the wavelength 800 nm and 400 nm corresponding to ω and 2ω, respectively.

Ray et al. have observed a very strong asymmetry in the emission of D+ ions from D₂ (see Fig. 3.8), where relatively long∼45 fs linear polarized pulses were employed [73]. The experimental results were further interpreted in terms of a model based on the dynamic coupling of the gerade and ungerade states in the D+₂ molecular ion by the laser field [73]. The experiment shows a dependence of the phase-dependent asymmetry on the energy of the emitted ion (see Fig. 3.8). The asymmetries were associated with various dissociation channels including one-photon BS, visible between 0–0.3 eV, two-photon above-threshold dissociation (ATD) [39] with a strong signal in the range of 0.3–2 eV and rescattering (RES). The rescattering was introduced in this thesis as recollisional excitation (RCE). RES results in an asymmetry at high energies from 4 to 6 eV. The strong signal centered near an ion energy of 3 eV corresponds to CREI [87, 88] or enhanced ionization (EI), involving the double ionization of D2 and the generation of two deuteron ions and therefore no asymmetry is observed in this energy range, as is seen in Fig. 3.8.

3.5

Asymmetric dissociation of molecular hydrogen in

a two-color, attosecond XUV–femtosecond near-

IR field

Control of electron dynamics in molecular hydrogen can also be achieved using a pump- probe scheme: an attosecond extreme ultraviolet (EUV or XUV) pulse as the ”pump”

30 isotopes pulse and a weak, CEP-stabilized few-cycle near-IR pulse as the ”probe” pulse. Such a scheme was first implemented by Sansoneet al.[66] where electron charge localization was observed in the dissociative ionization of H₂ and D₂ molecules.

Isolated attosecond XUV pulses with a duration of 300–400 as extending from 20 to 40 eV [89] were generated through high-order harmonic generation (HHG) in krypton. The XUV pulses and time-delayed linear polarized IR pulses of 6 fs (FWHM) were crossed with an effusive H2 or D2 gas jet inside a VMI spectrometer [50] and the resulting H+ or D+ ions were detected. Fig. 3.9a shows measured kinetic energy distributions for D+fragments integrated over 45◦ along the laser polarization direction as a function of the time delayτ. The dominating process at low kinetic energies (W <1 eV) is the BS of the bound X2Σ+_g state of D+₂ caused by the near-IR pulse. The signal attributed to the vibrational wave packet peaks nearτ ≈+11 fs in good agreement with previous results on vibrational wave packet motion in the D+₂ ground state [31]. When the XUV and near-IR pulses overlap (τ ≈ 0 fs), the D+ signal strongly increases around 8 eV. The enhancement of the signal at high energies can be attributed to a growth in the excitation cross-section of the A2Σ+_u continuum state caused by infrared-laser-induced mixing of the A2Σ+_u and X2Σ+_g states. The increase may also contain contributions from photoionization of the Q11Σ+u doubly

excited autoionizing states by the near-IR laser. Fig. 3.9b shows the asymmetry of D+ ion emission in opposite directions along the laser polarization vector. The time-dependent asymmetry parameter A(W, τ), as defined in Eq. 3.11 and obtained by integration of the fragment emission overα= 45◦, exhibits pronounced oscillations as a function of the delay between the pump and probe pulses τ.

Recent progress in computational methods allows the inclusion of excited neutral states of H₂ that can be reached in the ionization (e.g. by a XUV pulse) and then decay via autoionization [90]. To solve a complex case of XUV–near-IR pump-probe dynamics in H2 [66] full dimensional integration of the TDSE was used. Comparison of the experiment to the calculations for ionization of H2 reveals two main mechanisms responsible for the observed asymmetry oscillations. For the small delays when the pump and the probe pulses overlap (τ <8 fs) the few-cycle near-IR field influences the photoexcitation process as illustrated in Fig. 3.10a. Excitation of H2 molecule involving absorption of XUV and near-IR photons can produce a wave packet in the A2Σ+_u state. At the same time the XUV pulse can excite the Q11Σ+u state, which can subsequently autoionize into the X2Σ+g

state. At larger pump-probe delays the IR pulse can induce population transfer between the A2Σ+_u and X2Σ+_g states (see Fig. 3.10b). The interference between the A2Σ+_u and X2Σ+_g wave packets results in the observed asymmetry.

3.5 Asymmetric dissociation of molecular hydrogen in a two-color, attosecond

XUV–femtosecond near-IR field 31

Figure 3.9: Experimentally measured (a) kinetic energy distributions and (b) asymmetry parameter for the formation of D+ ions in two-color attosecond XUV–femtosecond near-IR dissociative ionization of D2, as a function of the fragment kinetic energyW and the delay between the pump and probe pulses τ. Adapted from [66].

Figure 3.10: Mechanisms that lead to asymmetry in XUV–near-IR dissociative ionization (adapted from Ref. [66]). (a) Mechanism I: asymmetry caused by the interference of a wave packet launched in the A2Σ+_u state by direct XUV ionization or rapid ionization of the Q11Σ+u doubly-excited autoionizing states by the IR pulse and a wave packet in

the X2Σ+_g state resulting from autoionization of the Q₁1Σ+_u states. (b) Mechanism II: asymmetry caused by the interference of a wave packet in the A2Σ+_u populated by direct XUV ionization and a wave packet in the X2Σ+_g state that results from stimulated emission during the dissociation process. Blue and red arrows indicate the XUV and near-IR pulses correspondingly. Molecular dynamics are marked by purple lines.

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