FIG 2 - uploaded by Pascal Salieres
Content may be subject to copyright.
Excursion time calculated for each trajectories within laser peak intensity of I0 = 0.5−2×10 14 W.cm −2 as employed in the experiment and shown in the colour bar. The mapping law for both trajectories allows us to follow dynamical process from 200 asec to 1.7 fsec for the short trajectory and from 1.7 fsec to 2.7 fsec for the long trajectory
Source publication
We investigate how short and long electron trajectory contributions to high
harmonic emission and their interferences give access to intra-molecular
dynamics. In the case of unaligned molecules, we show experimental evidences
that the long trajectory signature is more dependent upon the molecule than the
short one, providing a high sensitivity to c...
Context in source publication
Context 1
... our experimental conditions (800 nm and I 0 = 0.5 − 2 × 10 14 W.cm −2 ), we present the mapping law in figure 2. As one can see depending on the laser peak intensity I 0 (colorbar) the cutoff extends toward higher harmonic order as expected. For the maximum extension (we employed a maximum peak intensity of 2 × 10 14 W/cm 2 ) the short trajectory maps a time scale from ∼ 200 asec to the position of the excursion time of the cutoff 1.7 fsec whereas the long trajectory maps a time scale from the cutoff excursion time (1.7 fsec) to ∼ 2.7 fsec. Thus, if any intra-cation dynamics oc- curs within this time window, the total dipole moment is modified dictating that the HHG radiation encodes key signatures of this motion just after ionisation 9,11 . We will indeed examine the case of fast nuclear motion, channel superposition signature and channels dynamical popula- To access the encoded information, experimental meth- ods based on HHG have been employed. The PACER technique (Probing Attosecond motion by Chirp En- coded Recollision), that accesses the cation dynamics via the time-frequency mapping allowed by the attosecond chirp, was first implemented for retrieving nuclear dy- namics by comparing the HHG spectrum between deuter- ated (reference) and protenated molecules of the same species 10,11 . The tomography technique 12-14 permits to access information on which ground states (molecular or- bitals) is involved in the HHG process and for this a normalisation to an atomic partner response (reference) is required. Recent works 15 based on two HHG source interferometry, one source in unaligned molecules (ref- erence) and the other one in aligned molecules, shows that the HHG signal contains crucial information on the electronic orbitals involved in the process and their fast dynamics. The ideal tool would be to access these dy- namics without recourse to an auxiliary reference to ex- tend the possibility of such pump-probe scheme to reveal in a more versatile way the dynamical ...
Similar publications
Rescattering effects in nonresonant spontaneous laser-assisted electron-atom
bremsstrahlung (LABrS) are analyzed within the framework of time-dependent
effective-range (TDER) theory. It is shown that high energy LABrS spectra
exhibit rescattering plateau structures that are similar to those that are
well-known in strong field laser-induced processe...
Citations
... This would require changing the pump-probe delay in the experiment, while keeping fixed the laser intensity and wavelength, as well as the de Broglie wavelength of the electron. In this Letter, we show that this can be achieved by making use of a wellknown property of HHG: each harmonic is emitted by two electron quantum paths (QPs) labeled short and long, that have spent very different travel times in the continuum [9,36] and thus probe the target with the same de Broglie wavelength, at the same driving laser intensity, but at different delays [37]. The contributions from these two QPs can be distinguished in spatially resolved harmonic spectra [38,39]. ...
Strong-field ionization of molecules releases electrons which can be accelerated and driven back to recombine with their parent ion, emitting high-order harmonics. This ionization also initiates attosecond electronic and vibrational dynamics in the ion, evolving during the electron travel in the continuum. Revealing this subcycle dynamics from the emitted radiation usually requires advanced theoretical modeling. We show that this can be avoided by resolving the emission from two families of electronic quantum paths in the generation process. The corresponding electrons have the same kinetic energy, and thus the same structural sensitivity, but differ by the travel time between ionization and recombination—the pump-probe delay in this attosecond self-probing scheme. We measure the harmonic amplitude and phase in aligned CO2 and N2 molecules and observe a strong influence of laser-induced dynamics on two characteristic spectroscopic features: a shape resonance and multichannel interference. This quantum-path resolved spectroscopy thus opens wide prospects for the investigation of ultrafast ionic dynamics, such as charge migration.
... Its consequent recombination induces an oscillating dipole, which imprints its amplitude and phase on the emitted HHG photons [8]. This ultrafast HHG process occurs in less than half of a laser oscillation period giving the potential to explore sensitive measurement on molecular electron structure and nuclear dynamics known as high-harmonic spectroscopy [9][10][11][12][13]. ...
High-harmonic spectroscopy can access structural and dynamical information on molecular systems encoded in the amplitude and phase of high-harmonic generation (HHG) signals. However, measurement of the harmonic phase is a daunting task. Here, we present a precise measurement of HHG phase difference between two isotopes of molecular hydrogen using the advanced extreme-ultraviolet (XUV) Gouy phase interferometer. The measured phase difference is about 200 mrad, corresponding to ~3 attoseconds ( 1 as = 10 − 18 s ) time delay which is nearly independent of harmonic order. The measurements agree very well with numerical calculations of a four-dimensional time-dependent Schödinger equation. Numerical simulations also reveal the effects of molecular orientation and intramolecular two-center interference on the measured phase difference. This technique opens a new avenue for measuring the phase of harmonic emission for different atoms and molecules. Together with isomeric or isotopic comparisons, it also enables the observation of subtle effects of molecular structures and nuclear motion on electron dynamics in strong laser fields.
... To explain in more details the finer aspects of CM goes beyond the scope of this study. Nevertheless, QPI effects depend strongly on the phase accumulated by the electronic wave packet in the continuum, which is a strong function of the intensity and the temporal shape of the laser field in general supporting the validity of the SFA in studying QPI [30,[55][56][57]. Hence, in a differential intensity resolved measurement, such as the one carried out in our work, one would expect that the QPI features would be retained. ...
We investigate the electron quantum path interference effects during high harmonic generation in atomic gas medium driven by ultrashort chirped laser pulses. To achieve that, we identify and vary the different experimentally relevant control parameters of such a driving laser pulse influencing the high harmonic spectra. Specifically, the impact of the pulse duration, peak intensity and instantaneous frequency is studied in a self-consistent manner based on Lewenstein formalism. Simulations involving macroscopic propagation effects are also considered. The study aims to reveal the microscopic background behind a variety of interference patterns capturing important information both about the fundamental laser field and the generation process itself. The results provide guidance towards experiments with chirp control as a tool to unravel, explain and utilize the rich and complex interplay between quantum path interferences including the tuning of the periodicity of the intensity dependent oscillation of the harmonic signal, and the curvature of spectrally resolved Maker fringes.
... High harmonic spectroscopy [1][2][3] can access structural and dynamical information on molecular systems encoded in amplitude and phase of high harmonic generation (HHG) signals [4][5][6][7][8][9]. However, measurement of the harmonic phase is a daunting task. ...
High harmonic spectroscopy can access structural and dynamical information on molecular systems encoded in amplitude and phase of high harmonic generation (HHG) signals4. However, measurement of the harmonic phase is a daunting task. Here we present a precise measurement of HHG phase difference between two isotopes of molecular hydrogen using the advanced extreme-ultraviolet (XUV) Gouy phase interferometer. The measured phase difference is about 200 mrad, corresponding to 3 attoseconds (1 as = 10^-18 s) time delay which is nearly independent of harmonic order. The measurements agree very well with numerical calculations of a four-dimensional time-dependent Schroedinger equation. Numerical simulations also reveal the effects of molecular orientation and intra-molecular two-centre interference on the measured phase difference. This technique opens a new avenue for measuring the phase of harmonic emission for different atoms and molecules. Together with isomeric or isotopic comparisons it also enables the observation of subtle effects of molecular structures and nuclear motion on electron dynamics in strong laser fields.
... To explain in more details the finer aspects of CM goes beyond the scope of this study. Nevertheless, QPI effects depend strongly on the phase accumulated by the electronic wave packet in the continuum, which is a strong function of the intensity and the temporal shape of the laser field in general supporting the validity of the SFA in studying QPI [30,[55][56][57]. Hence, in a differential intensity resolved measurement, such as the one carried out in our work, one would expect that the QPI features would be retained. ...
We investigate the electron quantum path interference effects during high harmonic generation in atomic gas medium driven by ultrashort chirped laser pulses. To achieve that, we identify and vary the different experimentally relevant control parameters of such a driving laser pulse influencing the high harmonic spectra. Specifically, the impact of the pulse duration, peak intensity and instantaneous frequency is studied in a self-consistent manner based on Lewenstein formalism. Simulations involving macroscopic propagation effects are also considered. The study aims to reveal the microscopic background behind a variety of interference patterns capturing important information both about the fundamental laser field and the generation process itself. The results provide guidance towards experiments with chirp control as a tool to unravel, explain and utilize the rich and complex interplay between quantum path interferences including the tuning of the periodicity of the intensity dependent oscillation of the harmonic signal, and the curvature of spectrally resolved Maker fringes.
... The emergence of attosecond pulses [1,2] enabled scientists entering a new era, in which one can observe, trace, and control the fastest events in matter with unprecedented-attosecond (as)-temporal resolution [3][4][5][6][7][8][9][10][11]. Over the past twenty years, attosecond pulses were used as a fast camera shutter to resolve and investigate ultrafast dynamical events [12][13][14], such as time delay of photoemission [15,16], electron dynamics in molecules [17,18], electron-electron correlation in strongfield [19,20], dynamics of nanoparticles excited by few cycle laser [21][22][23][24], petahertz electronics in gas [25] and solid [26] with unprecedented temporal accuracy down to 10 as [27,28], chemical reactions [29,30], coincidence information of ultrafast mass spectroscopy [31], and probing strong field quantum optics in gaseous [32] and condensed matter [33]. However, until now the repetition rate of most of the attosecond sources was limited to few kHz, which hindered many applications. ...
We generate attosecond pulse train (APT) in argon driven by the high repetition rate (HR) laser of the extreme light infrastructure-attosecond light pulse source (ELI-ALPS), providing 100 kHz, 80 W, 1030 nm, 40 fs pulses from a fiber chirped-pulse amplification (fiber-CPA) laser system. Under the current operating conditions of the high harmonic generation beamline (HR-GHHG), we observed the average pulse duration to be 395 as measured using the technique of reconstruction of attosecond beating by interference of two-photon transitions. The beamline uses an annular-shape laser beam so that the main part of the driving laser co-propagating with the APT can be eliminated by reflection on a holey mirror. An additional 100 nm aluminum foil is used to filter out the remaining laser and the low order harmonics, allowing 2 pJ APT with a bandwidth from 25 eV to 50 eV to be transported to the target position where the APT interacts with matter. The implementation of the HR-GHHG beamline in ELI-ALPS delivering attosecond pulse trains at 100 kHz paves the way for time-resolved experiments in the infrastructure, especially those that involve rare events and coincidence analysis, both of which need high statistics.
... Recent theoretical calculations have shown that a way to overcome this obstacle and purify the results is to develop a direct measurement approach (a method which does not need the use of auxiliary atomic references) based on the use of S and L quantum path interferences in a molecular system [36]. However, such interferences were never observed experimentally in a molecular system and hence their applicability on attosecond spectroscopy remained an open question. ...
... In these calculations the appearance of the doubleand single-peak structure is found to be at τ (double) calc ≈ 4.13 ps and τ (single) calc ≈ 4.3 ps, respectively, which is in fair agreement with the experimental values. The deviation observed between τ expt and τ calc might originate from the contribution of highorder harmonics generated by other molecular orbitals (such as HOMO-1, HOMO-2) [36]. However, this matter requires more elaborative considerations of multielectronic molecular structure which is out of the scope of the present work. ...
... It is found that the phase difference between the S and L quantum paths is shifted by a value larger than π when the molecular axis is changing from parallel to perpendicular with respect to the polarization of the laser field. These findings, besides the fundamental interest on carrying out investigations in aligned diatomic molecules, in conjunction with longer wavelength-driven molecular-HHG schemes and coincidence detection arrangements, can be used for the development of self-referenced attosecond spectroscopy approaches [36,57] and the recently demonstrated laser-driven electron diffraction schemes [58,59]. S.C., I.L., and E.S. equally contributed to the experiment and data analysis; S.K. contributed in the experiment and the theoretical calculations; M.U.K. and N.T. performed the theoretical calculations; O.F. developed the pump-probe arrangement and contributed to data analysis and manuscript preparation; N.P. developed the data acquisition system; B.W. and D.C. contributed to data analysis and manuscript preparation; P.T. conceived the idea, supervised the project, wrote the manuscript, and contributed to all aspects of the work. ...
Electron quantum path interferences in strongly laser-driven aligned molecules and their dependence on the molecular alignment is an essential open problem in strong-field molecular physics. Here, we demonstrate an approach which provides direct access to the observation of these interference processes. The approach is based on the combination of the time-gated-ion-microscopy technique with a pump-probe arrangement used to align the molecules and generate high-order harmonics. By spatially resolving the interference pattern produced by the spatiotemporal overlap of the harmonics emitted by the short and long electron quantum paths, we have succeeded in measuring in situ their phase difference and disclose their dependence on molecular alignment. The findings constitute a vital step towards an understanding of strong-field molecular physics and the development of attosecond spectroscopy approaches without the use of auxiliary atomic references.
... In practice, the influence of the electron dynamics on a structural interference could be observed by following the phase difference between the short or long trajectory contributions when varying the laser intensity, e.g., by recording the quantum path interferences (QPI) in the total harmonic dipole [83,84]. We performed such an analysis in our TDSE simulations, and we show the results in Fig. 8(a) for both the molecule and the reference atom. ...
... Finally, as the phases of the short and long trajectories evolve differently, an interferometric experimental setup based on quantum path interferences [83,84] should be able to reveal their signatures. ...
We study the signature of two-center interferences in molecular high-order harmonic spectra, with an emphasis on the spectral phase. With the help of both ab initio computations based on the time-dependent Schrödinger equation and the molecular strong-field approximation (SFA) as developed by Chirilă et al. [Phys. Rev. A 73, 023410 (2006)] and Faria [Phys. Rev. A 76, 043407 (2007)], we observe that the phase behavior is radically different for the short and the long trajectory contributions. By means of Taylor expansions of the molecular SFA, we link this effect to the dynamics of the electron in the continuum. More precisely, we find that the value of the electric field at recombination time plays a crucial role in the shape of the destructive interference phase jump.
... In practice, the influence of the electron dynamics on a structural interference could be observed by following the phase difference between the short/long trajectory contributions when varying the laser intensity, e.g., by recording the Quantum Path Interferences (QPI) in the total harmonic dipole [84,85]. We performed such an analysis in our TDSE simulations and show the results in Fig. 8(a), for both the molecule and the reference atom. ...
... Finally, as the phases of the short and long trajectories evolve differently, an interferometric experimental setup based on Quantum Path Interferences [84,85] should be able to reveal their signatures. ...
We study the signature of two-center interferences in molecular high-order harmonic spectra, with an emphasis on the spectral phase. With the help of both ab initio computations based on the time-dependent Schr\"odinger equation and the molecular Strong-Field Approximation (SFA) as developed by Chirila et al. [Physical Review A, 73, 023410 (2006)] and Faria [Physical Review A, 76, 043407 (2007)], we observe that the phase behavior is radically different for the short and the long trajectory contributions. By means of Taylor expansions of the molecular SFA, we link this effect to the dynamics of the electron in the continuum. More precisely, we find that the value of the electric field at recombination time plays a crucial role on the shape of the destructive interference phase-jump.
... In the previous work, 19 we showed that the HHG spectrum generated in the velocity gauge is in agreement with the semi-classical three-step model that has been confirmed by experimental results. 46 In the mentioned work, it has been shown that the HHG spectrum generated in the velocity gauge for N 2 molecule is in good agreement with the experimental finding (Fig. 4 in Ref. 46). However, to obtain information about the molecular structure such as the orbital tomographic and position of dips, the acceleration gauge is preferable. ...
... In the previous work, 19 we showed that the HHG spectrum generated in the velocity gauge is in agreement with the semi-classical three-step model that has been confirmed by experimental results. 46 In the mentioned work, it has been shown that the HHG spectrum generated in the velocity gauge for N 2 molecule is in good agreement with the experimental finding (Fig. 4 in Ref. 46). However, to obtain information about the molecular structure such as the orbital tomographic and position of dips, the acceleration gauge is preferable. ...
In the present work, an efficient method is theoretically investigated for extending high-order harmonics and ultrashort attosecond pulse generation in N2 and CO molecules by using the time-dependent density functional theory approach. Our results show that by utilizing chirped laser field in the presence of a low frequency field, not only is the harmonic cutoff extended remarkably but also the single short quantum trajectory is selected to contribute to the harmonic spectra. When a low frequency field is added to the two-color chirped laser field, the long quantum trajectories are suppressed and only the short quantum trajectories contribute to the higher harmonic emission mechanism. As a result, the spectral modulation is significantly decreased and an intense ultrashort pulse can be generated from the supercontinuum region of high harmonics. With such a scheme, the isolated ultrashort attosecond pulses can be generated in length, velocity, and acceleration gauges. Furthermore, these results are explained by using the classical and quantum time-frequency analyses.
