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300 attosecond response of acetylene in two-photon ionization/dissociation processes

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Abstract

By performing delay scans of two replicas of a few-pulse attosecond pulse train (APT), we investigated two-photon ionization/dissociation processes of ${{\rm{C}}_2}{{\rm{H}}_2}$. The correlation time of the ${{\rm{C}}^ +}$ yield is determined to be 300 as, which is, to the best of our knowledge, the shortest correlation time ever obtained in the delay-scan measurement of two APTs. We also extracted the contribution of the resonant excitation from the ground state to a specific excited state of ${{\rm{C}}_2}{\rm{H}}_2^ +$ leading to C–C bond breaking by performing Fourier analyses of the yield and angular distribution of the ${{\rm{CH}}^ +}$ fragment ions, which are also generated within 300 as.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

The high-order harmonic (HH) fields generated from femtosecond laser pulses are regarded as table-top light sources, providing short-wavelength light pulses reaching vacuum ultraviolet (VUV), extreme ultraviolet (XUV), and even soft x-ray wavelength regions [1,2]. The spectral frequency ranges of the HH fields are generally wider than 1 PHz, and these fields are coherently superposed. Thus, they form a bunch of pulses with a duration of less than 1 fs in the time domain, which is called an attosecond pulse train (APT) [35]. Pulses in an APT last for a few femtoseconds or even longer, depending on the duration of the driving fundamental laser pulse, whereas the repetition period of attosecond pulses is kept to half the period of the optical field of the fundamental pulse. Owing to the ultrashort pulse duration and high photon energy, APTs are suitable for the study of ultrafast molecular dynamics with a time scale of femtoseconds [614] or even a shorter time scale of attoseconds [1518]. In these previous studies, an APT was used as a pump to initiate dynamical processes of a molecule and/or as a probe to resolve the ultrafast motions of electrons or nuclei after pump pulse irradiation.

This is a typical experimental scheme known as the “pump-and-probe” scheme to reveal the temporal variations of the states in a target molecule. On the other hand, the pump-and-probe scheme can also be applied to the characterization of an APT itself. For example, by scanning the delay between an XUV HH pulse and a fundamental laser pulse, we can determine the spectral phase difference between harmonic fields with adjacent orders by observing the modulation of the sideband electron yield originating from the two-color above-threshold ionization of rare gas atoms [4,19]. This kind of technique for the measurement of a cross correlation between an HH pulse and a fundamental pulse is nowadays being developed to characterize an isolated attosecond pulse (IAP) with the help of the reconstruction algorithm developed for the frequency-resolved optical gating (FROG) technique [2022].

By applying the two replicas of the same HH pulse for both pump and probe pulses, we can obtain the trace of the signal yield by the delay scan that is exactly the same as an autocorrelation (AC) trace, which exhibits the temporal profile of the APT as long as the signal is generated with the nonlinear interaction of two APTs and the response time for the signal yield is much shorter than the duration of each attosecond pulse in the train. Since the first demonstration of the AC measurement of HH pulses more than 20 years ago [23], this measurement technique has been improved to provide important features of APTs [5,24,25] and an IAP [2628]. The ultrafast evolutions of a quantum wave packet in the femtosecond regime, as well as in the attosecond regime, were also revealed by these AC measurement techniques [11,1518]. In particular, the interferometric AC (IAC) technique, by which we can resolve the optical interference fringes of XUV harmonic fields appearing on an IAC trace, is useful in finding such ultrafast dynamics in molecules because the Fourier analysis of the modulations in IAC traces gives us information about the electronic states involved in a nonlinear optical process yielding fragment ions. We call this method “nonlinear Fourier transform spectroscopy” (NFTS).

In this paper, we report on the IAC measurements of an APT performed by detecting the fragment ions generated from acetylene (${{\rm{C}}_2}{{\rm{H}}_2}$) using a velocity map imaging (VMI) ion spectrometer. The IAC traces obtained by monitoring the three kinds of fragment ion yields (${{\rm{C}}^ +}$, ${{\rm{CH}}^ +}$, and ${{\rm{H}}^ +}$) all exhibited XUV interference fringes originating from attosecond bunches in an APT envelope. The correlation time of the attosecond pulses obtained from the ${{\rm{C}}^ +}$ yield was estimated to be 300 as, which is, to the best of our knowledge, the shortest correlation time in the AC measurement of an APT. The fast response of the ${{\rm{C}}^ +}$ yield should be attributed to non-sequential ionization/dissociation processes induced by the two-photon absorption in the APT composed of VUV–XUV harmonic fields in the photon energy range between 7 and 21 eV.

In addition, we found that sequential ionization and dissociation processes contribute to the ${{\rm{CH}}^ +}$ yield by resonant excitation via a specific electronically excited state, leading to the breaking of the C–C chemical bond. We obtained experimental evidence of this process by applying the Fourier analyses to both an IAC trace of the yield of ${{\rm{CH}}^ +}$ and that of the anisotropy parameter characterizing the angular distribution of ${{\rm{CH}}^ +}$ measured using the VMI ion spectrometer. Although the process includes the resonant excitation from the ground state to the excited ${3^2}{\Pi _{\rm{g}}}$ state of ${{\rm{C}}_2}{\rm{H}}_2^ +$, the correlation time of the IAC trace of the ${{\rm{CH}}^ +}$ yield was found to be as short as about 300 as, suggesting that the yield of ${{\rm{CH}}^ +}$ exhibiting the correlation originates from non-sequential excitation processes. Thus, we successfully discriminated the non-sequential excitation processes yielding ${{\rm{CH}}^ +}$ from the competing sequential processes by NFTS.

In the following sections, we will briefly describe the experimental setup, introduce the recorded IAC traces, discuss the results of the analyses, and give a conclusion of this study.

2. EXPERIMENT

The experimental setup is similar to that reported in refs. [11,17,18]. A Ti:sapphire chirped-pulse amplification system [29] delivers driving laser pulses with a pulse energy of 20 mJ, a pulse duration of 12 fs, and a repetition rate of 100 Hz. The driving laser pulses are loosely focused ($f = 5 \;{\rm{m}}$) onto a gas cell filled with Xe to generate an intense high-harmonic beam [30] or equivalently an APT, which propagates with a driving laser pulse in a vacuum tube until it passes through an aperture with a diameter of 2 mm placed 4 m away from the gas cell.

APTs are spatially split into two replicas by a pair of Si beam splitter mirrors (SiBSs) [24,28] situated as closely as possible. The incident angle to the beam splitter is set to be 75° so as to attenuate the intense driving laser pulse to less than ${10^{- 3}}$ under the Brewster condition, whereas the reflected APT in the UV–XUV wavelength region is not reduced significantly owing to a relatively high reflectivity (${\sim}0.5$) of the Si mirror in this wavelength region. The temporal delay between the two APT replicas is adjusted by changing the position of one of the Si mirrors mounted on a translation stage using a piezoelectric actuator.

After reflection by a pair of Si mirrors, two APTs are introduced into a VMI spectrometer chamber [31] and focused into ${{\rm{C}}_2}{{\rm{H}}_2}$ as the molecular gas beam injected through a pinhole drilled at the center of a repeller electrode used as part of the electrostatic lens to image a velocity map of ions onto an ion detector. The gas jet pulses supplied by a pulsed valve [32] are synchronized with the laser shots applied. A SiC concave mirror with a curvature radius of 200 mm is used to focus the two APTs. The fragment ions generated are accelerated and focused by an electrostatic lens on a position-sensitive detector composed of two microchannel plates (MCPs) with chevron stacking and a phosphor screen. Fluorescent images on the phosphor screen are recorded by a CMOS camera and the counting detection [33] is performed. We can separate a fluorescent image of one fragment ion species from those of other species by applying a pulsed high voltage to the MCPs at the time-of-flight of the targeted fragment ion species.

We acquired 500 images of the targeted fragment ion species at each delay time in a single scan. The scanning range of the delay was set to be from ${-}{{7}}$ to 7 fs to reveal the entire train envelope of the APT, which is expected to be a few fs. The delay scan was implemented with scanning the position of the translation stage on which one of the SiBSs was mounted. The translation step was 20 nm, which was equivalent to the delay step of 35.8 as. This delay step was sufficiently small to resolve interference fringes of the 13th-order HH field, whose optical period was about 200 as. The relationship between the translation and the delay was calibrated by measuring the frequency of the spectral interference fringes of the third-harmonic pulses reflected from the pair of SiBSs upon scanning the position of the translation stage in a separate measurement. The delay scan was repeated 12 times for ${{\rm{CH}}^ +}$ and eight times for ${{\rm{C}}^ +}$ and ${{\rm{H}}^ +}$. We also scanned for ${{\rm{H}}^ +}$ with and without the injection of ${{\rm{C}}_2}{{\rm{H}}_2}$ alternatingly to distinguish the ${{\rm{H}}^ +}$ fragments originating from ${{\rm{C}}_2}{{\rm{H}}_2}$ from those originating from residual gases, generating the background signals. The recorded images at each delay were converted to slices of momentum spheres [34] to obtain the yields of fragment ions and the anisotropy parameter.

We measured the spectrum of the HHs with an XUV spectrograph placed behind the VMI spectrometer by removing the SiC concave mirror mounted on a linear-translation rod. The spectrum of the HH fields at the focal point of the SiC concave mirror is shown in Fig. 1. In drawing this figure, we estimated the fluence per unit photon energy from the measured HH spectra, the quantum efficiency of an x-ray CCD camera detecting the HH fields, the diffraction efficiency of a flat field grating in the XUV spectrograph, the reflectivity of the SiC concave mirror, and the beam diameter of the HH fields calculated from the aperture diameter. The spectra of the fundamental and third-harmonic pulses were obtained in separate experiments, in which we measured the spectra using the spectrometers in the visible and UV regions, respectively.

 figure: Fig. 1.

Fig. 1. Spectral fluence of an APT at the focus estimated from the HH spectrum and the fundamental and third-harmonic spectra.

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 figure: Fig. 2.

Fig. 2. (a) Delay-dependent signal intensities of ${{\rm{CH}}^ +}$ (left), ${{\rm{C}}^ +}$ (center), and ${{\rm{H}}^ +}$ (right) fragments. The signals of ${{\rm{CH}}^ +}$ and ${{\rm{C}}^ +}$ are obtained by integrating their yields in the kinetic energy range below 5 eV. The signal of ${{\rm{H}}^ +}$ is obtained by integrating its yield in the kinetic energy range below 8 eV. (b) Envelope autocorrelation traces of APTs in the three channels. The bandpass filter extracting even-order harmonic components from 0th to 8th is applied to the respective interferometric autocorrelation traces. Black dashed lines show the baselines. An error bar in each panel in (a) and (b) was evaluated by assuming the Poisson statistics of the number of ion fragments counted. We plot one representative error bar in each trace so that the trace will not be covered by many error bars. The error bar for each delay step was deviated only 20% at most from the representative error bar.

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3. RESULTS AND ANALYSIS

A. Autocorrelation Traces

1. Determination of Correlation Time

The delay-dependent yields of the ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ fragment ions are shown in the left, middle, and right panels, respectively, of Fig. 2(a) as a function of delay time. We find, by referring to the top axes, that bunches at every half period of the fundamental optical field ${T_0}$ appear in all the three traces. These bunches appearing in the IAC traces reflect the temporal intensity profile of the APT, because the attosecond pulses emerge at every ${T_0}/2$ in the APT. This characteristic feature also ensures that these fragment ions are generated by multi-photon absorption in the ionization/dissociation processes and that the response time of these processes is much shorter than the duration of the attosecond pulses in the APT. Note that the correlation trace obtained from the experiment does not exactly coincide with the autocorrelation trace of the APT when the response time cannot be neglected, as will be discussed in Section 3.A.2. However, we use the terminology AC by convention to represent the correlation measurement using two identical optical pulses throughout this paper.

In Fig. 2(a), we can also identify that the fine fringes enhance and sharpen the peak of the bunch appearing at the time of the integer multiple of ${T_0}$, whereas they produce a sharp dent in the bunch at the time of the odd half-integer multiple of ${T_0}$. These characteristic peak profiles appearing alternatingly at even and odd half-integer multiples of ${T_0}$ originate from the optical interference of the HH components in the APT. The enhancement of the bunch at $n{T_0} (n = 0, \, \pm 1,\, \pm 2, \ldots)$ originates from the constructive interference and the dent at $(n + 1/2){T_0}$ originates from the destructive interference between the HH components in the APT and the HH components in the delayed APT.

On the basis of the results of previous studies [18,24,3537], we assume that the two-photon absorption of the HH components mainly contributes to the delay-dependent part of the yields of these fragment ions and the multiphoton absorption processes in which more than two photons are involved can be neglected. Under this assumption, we extracted an envelope autocorrelation (EAC) trace in each IAC trace by applying a band-pass filter to eliminate the frequency components of the odd harmonics. In the Supplement 1, we define the EAC trace and explain the relationship between the IAC and EAC traces of an APT.

The resultant EAC traces of ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ are shown in the left, middle, and right panels of Fig. 2(b), respectively. We evaluated the full-width at half-maximum (FWHM) of the central peak in each correlation trace, which we call the correlation time ${T_{{\rm{pulse}}}}$, using the linear interpolation between the discrete delay steps. The correlation time of the ${{\rm{CH}}^ +}$ fragment ion was obtained to be $318 \pm 6$ as, and those of the ${{\rm{C}}^ +}$ and ${{\rm{H}}^ +}$ fragment ions were obtained to be $297 \pm 3$ and $365 \pm 4$ as, respectively. The uncertainties associated with these correlation times were estimated from the Poisson statistics for the linear interpolation.

It can be said from these results that the duration of the attosecond pulses in the APT is shorter than 300 as, and that the response time of the ionization process by which ${{\rm{C}}^ +}$ is generated from ${{\rm{C}}_2}{{\rm{H}}_2}$ should be shorter so that the correlation time of 300 as can be realized.

Owing to the wide range of the delay scan and the short duration of the driving fundamental laser pulse, we can estimate the correlation time of the train envelope of the APT from each of the EAC traces of ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ fragment ions. For each fragment channel, we first perform the inverse Fourier transform (IFT) of the even-order harmonic components and then superpose the resultant IFT traces as the envelope function of the envelope autocorrelation, which is plotted as a dotted curve in each panel of Fig. 2(b). The envelope durations ${T_{{\rm{env}}}}$ for the EAC traces for ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ fragment ions are determined to be ${\sim}6.0$, ${\sim}5.0$, and ${\sim}6.3\; {\rm{fs}}$, respectively. Somewhat shorter ${T_{{\rm{env}}}}$ for ${{\rm{C}}^ +}$ can be attributed to the broader bandwidths of higher-order harmonic fields because the appearance energy of ${{\rm{C}}^ +}$ is the highest among the three fragment channels, as stated in the next subsection.

2. Time-Domain Analysis: Attosecond Response

To analyze the characteristics of the EAC traces in the three fragmentation channels shown in Fig. 2(b), we calculate EAC traces using a model on the basis of the method reported in ref. [38]. In this model, we assume that the amplitude of transition to the electronically excited states of ${{\rm{C}}_2}{\rm{H}}_2^ +$, from which a fragment ion is generated, is simply proportional to the product of the optical fields of the two APTs, and we neglect molecular responses. One of the key features of this model is that it can take into account the spatial profile at the focal point of the two APTs exhibiting spatial interference fringes altered by the delay change. We obtain EAC signals by summing up the integrals of the spatial profiles. In addition to these features described in ref. [38], we adapt this model calculation to the HH spectra with a finite bandwidth around each harmonic peak to reproduce the finite temporal width of the train envelope of an EAC trace. The details of the model calculation are described in the Supplement 1. Thanks to the inclusion of the bandwidth, we can use the measured spectral profile shown in Fig. 1 as an input of the model calculation.

We aim to interpret the differences in correlation times among the three fragment channels in terms of the differences in two-photon energy threshold. Thus, we examine the variations in EAC traces using the appearance energies of ${{\rm{CH}}^ +} + {\rm{CH}}$ (21.4 eV), ${{\rm{C}}^ +} + {\rm{CH}} + {\rm{H}}$ (24.8 eV), and ${{\rm{H}}^ +} + {{\rm{C}}_2}{\rm{H}}$ (18.9 eV) [39] as three different two-photon energy thresholds.

By adopting the model, we can calculate the two-dimensional spatial profile of the EAC traces as a function of the sum of the energies of two photons contributing to the temporal profile in a similar manner to a FROG technique. Therefore, we can restrict the sum of the energies of the two photons to be larger than a given threshold energy. The EAC trace in which the energy threshold is ignored can be calculated by integrating the entire range of the sum of the energies of the two photons.

We adopt an energy of 24.8 eV for the appearance energy of ${{\rm{C}}^ +}$ originating from the three-body dissociation and neglect the contribution of the two-body dissociation (${{\rm{C}}^ +} + {{\rm{CH}}_2}$). This is because the isomerization from ${[{\rm{HCCH}}]^ +}$ to ${[{{\rm{H}}_2}{\rm{CC}}]^ +}$ proceeding in the bound ${\tilde A^2}\Sigma _{\rm{g}}^ +$ state of ${{\rm{C}}_2}{\rm{H}}_2^ +$ takes 52 fs [40,41], which is much longer than the correlation time of the train envelope in the middle panel of Fig. 2(b).

In the simulation, we vary the group delay dispersion (GDD) to find optimal conditions under which we can reproduce the experimental correlation times of the three fragment channels. We assume in this calculation that the Gaussian beam profile with a radius of 1 mm at half-maximum is spatially split into two beams. The width of the gap between the two split beams is set to be 100 µm.

The resultant correlation times ${T_{{\rm{pulse}}}}$ are shown as red, blue, and green circles in Fig. 3 when the two-photon energy thresholds 24.8, 21.4, and 18.9 eV, respectively, are adopted. The correlation time obtained without considering a two-photon energy threshold is plotted as black circles in the same figure. We also evaluate the correlation times by calculating the EAC traces without considering the spatial profile for comparison. The results with the four different two-photon energy thresholds are shown using the same color codes in Fig. 3.

 figure: Fig. 3.

Fig. 3. Correlation time (${T_{{\rm{pulse}}}}$) defined as the FWHM of the central peak in the EAC trace calculated as a function of GDD. The correlation times obtained using different two-photon energy thresholds (${E_{{\rm{th}}}}$) are plotted in black (${E_{{\rm{th}}}} = 0$ eV), green (${E_{{\rm{th}}}} = 18.9$ eV), blue (${E_{{\rm{th}}}} = 21.4$ eV), and red (${E_{{\rm{th}}}} = 24.8$ eV). Dotted curves: ${T_{{\rm{pulse}}}}$ obtained without considering the spatial profile. The color codes for the two-photon energy threshold are the same as those for the circles. The correlation times obtained from the experimental autocorrelation traces for the ${{\rm{C}}^ +}$, ${{\rm{CH}}^ +}$, and ${{\rm{H}}^ +}$ channels are indicated as starting points of the horizontal dotted red, blue, and green arrows, respectively. The vertical dotted arrows indicate the corresponding GDD values.

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We find in Fig. 3 that the correlation times depicted as circles are all consistently longer by ${\sim}10\%$ than those obtained without considering the spatial profile of the APT at the same GDD value. This tendency is independent of the two-photon energy thresholds. These results show that the spatial integration is essential in the simulation of the EAC recorded by an interferometer using spatially split light beams.

Before the comparisons among the three fragment channels, we will focus on the estimation of the pulse duration by comparing the simulated correlation time with the longest correlation time of 370 as for the ${{\rm{H}}^ +}$ channel. Because we neglect the response time of the molecular ionization and fragmentation, we have to attribute the broadening of the correlation time to the broadening of an attosecond pulse itself in the APT due to the dispersions inherent to the HHG process. The correlation time of the central peak calculated by assuming the Fourier limit APT with the two-photon energy threshold of 18.9 eV is approximately 250 as, and the correlation time increases monotonically with the GDD value, as shown with the green circles in Fig. 3. We find that the correlation time of ${\sim}370$ as is reproduced by assuming the GDD value to be approximately $8.9 \times {10^{- 33}}\; {{\rm{s}}^2}$. This estimated GDD value agrees reasonably well with that estimated in our previous study [25], even though it was approximately half of the values obtained by the cross-correlation measurements between HHs and fundamental pulses [4,19]. Thus, we evaluate the duration of the most intense attosecond pulse in the train to be 270 as by simulating the temporal shape of the APT using the measured spectrum and the estimated GDD value. Note that the GDD value of an APT is generally positive mainly because the emission time of the harmonic field originating from a short-trajectory electron is delayed by the increase in photon energy.

 figure: Fig. 4.

Fig. 4. FT spectra of the IAC traces obtained for the ${{\rm{CH}}^ +}$ (blue), ${{\rm{C}}^ +}$ (red), and ${{\rm{H}}^ +}$ (green) channels, which are scaled so that the integrated areas in the range between 1 and 25 eV become the same.

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Next, we examine the traces with the different two-photon energy thresholds, depicted as red, blue, green, and black circles in Fig. 3, to find whether the change in energy threshold can consistently alter the correlation times of the ${{\rm{CH}}^ +}$ (320 as) and ${{\rm{C}}^ +}$ (300 as) channels compared with the ${{\rm{H}}^ +}$ (370 as) channel. Contrary to our expectations, the deviations of the correlation times among the four different two-photon energy thresholds at the same GDD value are estimated to be only ${\sim}2\%$ at most, and we conclude that the change in two-photon energy threshold does not significantly vary the correlation time as long as the threshold energy is lower than 24.8 eV. In other words, we cannot explain the reason why the correlation time takes different values depending on the decomposition channel only by taking into account the differences in the appearance energies of the ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ channels.

Therefore, it is possible that the correlation time is affected by the molecular response. As mentioned in ref. [38], the yields of fragment ions depend on the second-order transition amplitude between the electronic states of molecules. The assumption that the fragment yield is proportional to the square of the APT intensity, under which the EAC traces are calculated in this study, is equivalent to an assumption that transition amplitudes are the same in all ionization and dissociation pathways. Therefore, as the next step, we need to understand how molecular responses are incorporated to the calculation of EAC traces to explain the difference in correlation times, which will help us obtain an insight into attosecond dissociative ionization dynamics. In Section 1.3 in the Supplement 1, we explain how the molecular response affects the measured correlation time and show that the ion fragment yield should coincide with the autocorrelation function of an APT when the molecular response is instantaneous.

B. Nonlinear Fourier Transform Spectroscopy

1. General Features of Fourier Transform Spectra of IACs

To find spectroscopic features characteristic of the respective yields of the three different fragment ion species, we compute the Fourier transform (FT) of the IAC traces of the fragment ion yields shown in the panels in Fig. 2(a). The resultant magnitudes of the FT spectra of ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ channels are depicted in the left, middle, and right panels in Fig. 4, respectively. The frequency is converted to photon energy and the equivalent harmonic order is indicated on the top axes in these panels. The spectra are scaled by the area in the range from 1 to 25 eV so that we can compare the relative heights of peaks of the harmonics with the different orders in the different channels.

All the three FT spectra exhibit peaks at odd multiples of the fundamental frequency up to the 13th-harmonic order and the even multiples up to the eighth-harmonic order. The odd-order peaks manifest the interference of odd-order harmonics composing APTs. On the other hand, the peaks appearing at even multiples originate from the different frequency components between the two HHs having the different orders involved in the two-photon dissociative ionization processes.

2. Discrimination of Frequency Components

While the envelope autocorrelations, which are composed of even-order frequency components in the interferometric autocorrelations, mainly manifest the temporal profile of APT, the interference fringes modulated with odd-order frequencies can provide us with the spectroscopic information of molecules in addition to the optical interferences. In order to discriminate spectroscopic information from the optical interferences, we use the FT of the IAC trace obtained by the method described in Section 3.A.2.

In the bottom panel of Fig. 5(a), we compare the FT spectrum of the IAC trace in the ${{\rm{C}}^ +}$ channel (a profile with the red shaded area) with that of the IAC trace obtained by model calculation in which a Gaussian APT spatial profile is taken into account (a profile drawn with the purple solid line) and that obtained by model calculation in which an APT spatial profile is not taken into account (a profile drawn with the orange solid line). In model calculations, the GDD value is assumed to be $1.0 \times {10^{- 32}}\; {{\rm{s}}^2}$ and the two-photon energy threshold is assumed to be 24.8 eV. All the three spectra are normalized as described in Section 3.B.1. The top panel of Fig. 5(a) shows the peak area of the harmonic components in the FT spectra in the three cases in the bottom panel.

 figure: Fig. 5.

Fig. 5. (a) Bottom panel: The FT spectrum of the IAC trace for ${{\rm{C}}^ +}$ channel, which is the same as that shown in the middle panel of Fig. 4, is depicted as a red shaded area. The FT spectra of the IAC traces obtained by model calculations with and without considering the spatial profiles of the APT are depicted as purple and orange solid curves, respectively. Upper panel: experimental peak areas of the respective harmonic components for the ${{\rm{C}}^ +}$ channel (red shaded area) are plotted with red circles. The peak areas obtained by model calculation in which the spatial profiles of the APT are taken into account (purple circles) and those obtained by neglecting the spatial profiles of APT (orange circles) are also shown. The FT spectra are calculated with the GDD value of $1.0 \times {10^{- 32}}\; {{\rm{s}}^2}$ and the threshold energy of 24.8 eV. (b) Peak areas of the respective harmonic components relative to those obtained by model calculations. The scaled peak areas for the ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ channels are shown with blue solid triangles, red solid circles, and green solid squares, respectively.

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The deviations of the peak areas calculated without the APT spatial profile (orange circles) from those obtained from the ${{\rm{C}}^ +}$ channel at the harmonic orders 11th, 13th, and 15th are larger than those of the peak areas calculated using the Gaussian APT spatial profile (purple circles). Therefore, the FT spectrum of the IAC trace obtained using the Gaussian APT spatial profile can be used as a reference with which the frequency components originating from the optical interferences are extracted.

As shown in Fig. 5(b) with red filled circles, the peak area in the ${{\rm{C}}^ +}$ channel relative to that obtained by model calculation with the Gaussian APT spatial profile decreases monotonically as the harmonic order increases. In a similar manner, we derive the relative peak area as a function of the harmonic order for the ${{\rm{CH}}^ +}$ and ${{\rm{H}}^ +}$ channels as plotted in Fig. 5(b). In the calculations, the threshold energies of 21.4 and 18.9 eV are adopted for the ${{\rm{CH}}^ +}$ and ${{\rm{H}}^ +}$ channels, respectively.

The relative peak area of the harmonic component tends to decrease in the ${{\rm{CH}}^ +}$ and ${{\rm{H}}^ +}$ channels as the harmonic order increases similarly to that in the ${{\rm{C}}^ +}$ channel except at the seventh-harmonic component. Because the deviation at the seventh-harmonic component in the ${{\rm{CH}}^ +}$ channel is significant, we consider that the deviation originates from a resonant transition in the ionization/dissociation processes leading to the production of ${{\rm{CH}}^ +}$. This scenario is supported by the Fourier analyses of the anisotropy parameter for the three channels described in Section 3.B.3.

Note that the fundamental and third-harmonic components in the experimental FT spectra in the three fragment channels are all much larger than those obtained in the calculations, which may originate from resonant transitions induced by the fundamental and third-harmonic photons. ${{\rm{C}}_2}{{\rm{H}}_2}$ can be ionized through the absorption of the generated HHs (Fig. 1), not only to the ground state of ${{\rm{C}}_2}{\rm{H}}_2^ +$ but also to the ${\tilde A^2}\Sigma _{\rm{g}}^ +$ state and the higher-lying electronically excited states [42]. It is possible that the fundamental and third-harmonic components induce further electronic transitions from these electronically excited states of ${{\rm{C}}_2}{\rm{H}}_2^ +$ prepared by photoionization induced by the HHs, leading to the decomposition into fragments.

3. Fourier Transform of Anisotropy Parameter

We analyze the angular distributions of the fragment ions recorded using the VMI ion spectrometer. The angular distribution $F(\theta ,\tau)$ obtained from sliced images of fragment ions parallel to the detector plane is conventionally expanded in a series of even-order Legendre polynomials in terms of $\cos \theta$, where $\theta$ is the polar angle with respect to the polarization direction of the APT. Because the image varies with the change in the delay, $\tau$, the expansion coefficients should depend on $\tau$. Therefore, the angular distribution can be expressed as $F = F(\theta ,\tau) = R(\tau)[{1 + {\beta _2}(\tau){P_2}(\cos \theta) + {\beta _4}(\tau){P_4}(\cos \theta)}]$, where ${P_n} (n = 2 ,4)$ is the $n$th Legendre polynomial and ${\beta _2}$ is an anisotropy parameter. When ${\beta _2}$ is positive, the angular distribution of the fragment is enhanced along the direction parallel to the polarization direction. In contrast, when ${\beta _2}$ is negative, the angular distribution of the fragment is enhanced along the direction perpendicular to the polarization direction.

For all the three channels, we obtain ${\beta _2}(\tau)$ for the sliced image at each time delay and convert it by Fourier transform into the spectrum ${\tilde \beta _2}(\omega)$ in the angular frequency ($\omega$) domain. The real parts of ${\tilde \beta _2}(\omega)$, ${\rm{Re}}[{\tilde \beta _2}(\omega)]$, in the ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ channels are shown in the left, middle, and right panels in Fig. 6, respectively. When ${\rm{Re}}[{\tilde \beta _2}(\omega)]$ is positive, the oscillation at $\omega$ is in-phase with respect to the oscillation of the optical interference fringes, that is, ${\beta _2}(\tau) \propto \cos (\omega \tau)$. This indicates that the angular frequency component $\omega$ in HHs contributes to the enhanced fragmentation along the direction parallel to the polarization direction of the HHs. In contrast, a negative ${\rm{Re}}[{\tilde \beta _2}(\omega)]$, which represents ${\beta _2}(\tau) \propto - \cos (\omega \tau)$, indicates that the angular frequency component $\omega$ in the HHs contributes to the enhanced fragmentation along the direction perpendicular to the polarization direction of the HHs. Therefore, a strong positive peak at the angular frequency of the seventh harmonic ($7{\omega _0}$, with ${\omega _0}$ being the angular frequency of the fundamental laser light) in the ${{\rm{CH}}^ +}$ channel identified in the left panel in Fig. 6 shows that the $7{\omega _0}$ component enhances the fragmentation along the direction parallel to the polarization direction of the seventh harmonic. This enhancement shows that a parallel transition induced by the seventh harmonic produces ${{\rm{CH}}^ +}$ via the ionization/dissociation processes.

 figure: Fig. 6.

Fig. 6. Real parts of the Fourier transform spectra of the anisotropy parameter obtained for the ${{\rm{CH}}^ +}$ (left), ${{\rm{C}}^ +}$ (center), and ${{\rm{H}}^ +}$ (right) channels. The anisotropy parameters of the ${{\rm{CH}}^ +}$ and ${{\rm{C}}^ +}$ channels are obtained by integrating the fragment yields at kinetic energies below 1.5 eV and the anisotropy parameter of ${{\rm{H}}^ +}$ channel is obtained by integrating the fragment yield at kinetic energies below 3 eV.

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In Fig. 6, we also find prominent peaks at $3{\omega _0}$, $5{\omega _0}$, and $7{\omega _0}$ in the ${{\rm{C}}^ +}$ channel and a prominent peak at $3{\omega _0}$ in the ${{\rm{H}}^ +}$ channel, all of which may suggest that other resonant transitions are also involved in the fragmentation processes. These transitions are also expected to be parallel transitions on the basis of the same discussion as in the case of the $7{\omega _0}$ peak in the ${{\rm{CH}}^ +}$ channel. However, because we find no notable enhancement at these frequency components in the FT of the IAC traces shown in Fig. 5(b), it is difficult to discuss the origins of these prominent peaks. Therefore, we will concentrate on the origin of the distinct $7{\omega _0}$ peak in the ${{\rm{CH}}^ +}$ channel in the next subsection.

4. Ionization/Dissociation Pathway with a Resonant Transition

Although the dissociative ionization processes of ${{\rm{C}}_2}{{\rm{H}}_2}$ induced by a single XUV photon have been experimentally investigated [39,43], no experimental spectroscopic studies have been reported, to the best of our knowledge, on the dissociative ionization processes of acetylene in which two VUV–XUV photons are involved. Because the seventh harmonic enhances the production of ${{\rm{CH}}^ +}$ in the course of the two-photon excitation of ${{\rm{C}}_2}{{\rm{H}}_2}$, as explained in the preceding sections, the resonance absorption of the seventh harmonic occurs either within the neutral manifold prior to the ionization into ${{\rm{C}}_2}{\rm{H}}_2^ +$ or within the cation manifold after the ionization. As described in the Supplement 1, we can discard the possibility of the resonance absorption of the seventh harmonic in the neutral manifold. Therefore, we examine here how the resonance absorption is realized in the cation manifold. We performed theoretical calculation (see Supplement 1) to obtain the potential energy curves (PECs) of the low-lying excited states in ${{\rm{C}}_2}{\rm{H}}_2^ +$ along the C–C internuclear distance $r({\rm{CC}})$ along which C–C bond breaking to form ${{\rm{CH}}^ +}$ and CH can proceed, at the fixed internuclear distance of $r({\rm{CH}}) = 1.061$ Å for both ${\rm{C}} - {\rm{H}}$ bonds. The resultant PECs with their symmetry assignments are shown in Fig. 7. In Fig. 7, we also show the potential energies at $r({\rm{CH}}) = 1.061$ Å and $r({\rm{CC}}) = 1.203$ Å for the respective excited states obtained by Pitarch-Ruiz et al. [44] with an open circle. Indeed, the discrepancies from the potential energies we calculated are less than 0.11 eV for all the low-lying excited states. The equilibrium internuclear distances of ${{\rm{C}}_2}{{\rm{H}}_2}$, ${r_{\rm{e}}}({\rm{CC}}) = 1.203$ Å [45], is also shown with a gray vertical line.

 figure: Fig. 7.

Fig. 7. Theoretical potential energy curves of the low-lying electronic states of ${{\rm{C}}_2}{\rm{H}}_2^ +$ along the C–C internuclear distance $r({\rm{CC}})$. The two ${\rm{C}} - {\rm{H}}$ internuclear distances are fixed to be 1.061 Å. The gray vertical line represents the equilibrium C–C internuclear distance of neutral ${{\rm{C}}_2}{{\rm{H}}_2}$ at 1.203 Å. The gray shaded curve represents the probability distribution of the C–C internuclear distance of the vibrational ground level of the electronic ground state of neutral ${{\rm{C}}_2}{{\rm{H}}_2}$. The energy is the relative value with respect to that of the ${1^2}{\Pi _{\rm{u}}}$ state at 1.203 Å. Open circles represent the potential energies reported by Pitarch-Ruiz et al. [44] at $r({\rm{CH}}) = 1.061 $ Å and $r({\rm{CC}}) = 1.203 $ Å. The short horizontal bars on the right side of the figure represent the three lowest dissociation limits of ${{\rm{C}}_2}{\rm{H}}_2^ +$ [46,47].

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As shown in Fig. 7, the photon energy of the seventh harmonic (${\sim}11 \; {\rm eV}$) is in the range of the Franck–Condon projection (11–13 eV) of the Gaussian distribution of the C–C internuclear distance in the electronic ground ${1^2}{\Pi _{\rm{u}}}$ state, represented as the gray shaded area, to the repulsive part of the PEC of the ${3^2}{\Pi _{\rm{g}}}$ state, representing the anti-bonding character. In addition, the calculated absolute square of the transition dipole moment from the ground ${1^2}{\Pi _{\rm{u}}}$ state to the ${3^2}{\Pi _{\rm{g}}}$ state, $|\langle {{3^2}{\Pi _{\rm{g}}}|{\mu _{\parallel}}{{|1}^2}{\Pi _{\rm{u}}}}\rangle {|^2}$, is $14.9\, {{\rm{D}}^2}$ at $r({\rm{CC}}) = 1.203$ Å, which is approximately 2 orders of magnitude larger than those to the lower-lying excited ${1^2}{\Pi _{\rm{g}}}$ and ${2^2}{\Pi _{\rm{g}}}$ states, $|\langle {{1^2}{\Pi _{\rm{g}}}|{\mu _{\parallel}}{{|1}^2}{\Pi _{\rm{u}}}}\rangle {|^2} = 0.12 \,{{\rm{D}}^2}$ and $|\langle {{2^2}{\Pi _{\rm{g}}}|{\mu _{\parallel}}{{|1}^2}{\Pi _{\rm{u}}}}\rangle {|^2} = 0.16 \,{{\rm{D}}^2}$, respectively. Furthermore, the excess energy above the lowest dissociation limit of C–C bond breaking, ${{\rm{CH}}^ +}({X^1}{\Sigma ^ +}) + {\rm{CH}}({X^2}\Pi)$, located at 9.1 eV measured from the vibrational ground state in the electronic ground ${1^2}{\Pi _{\rm{u}}}$ state [47], is expected to be about 2 eV. This excess energy of about 2 eV corresponds to the kinetic energy of about 1 eV for the ${{\rm{CH}}^ +}$ fragment, which is consistent with the kinetic energy distribution of ${{\rm{CH}}^ +}$ recorded experimentally in this study. Therefore, it is highly probable that the enhancement at the seventh harmonic in the IAC trace for the ${{\rm{CH}}^ +}$ channel originates from the resonant transition from ${1^2}{\Pi _{\rm{u}}}$ to ${3^2}{\Pi _{\rm{g}}}$ in ${{\rm{C}}_2}{\rm{H}}_2^ +$ by the absorption of the seventh harmonic, leading to the production of ${{\rm{CH}}^ +}$ through C–C bond breaking. This means that the sequential process in which the one-photon ionization of ${{\rm{C}}_2}{{\rm{H}}_2}$ is followed by the resonant excitation proceeds simultaneously with the non-sequential two-photon processes responsible for the 320 as correlation time of the EAC trace in ${{\rm{CH}}^ +}$ channel.

4. CONCLUSION

We recorded the IAC traces of APTs by monitoring the ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ fragments generated via the dissociative ionization of ${{\rm{C}}_2}{{\rm{H}}_2}$. The IAC traces clearly exhibited the attosecond fringes and femtosecond train envelopes, manifesting the full temporal profile of the APTs. By removing the interference fringes from the measured IAC traces using a bandpass filter, we retrieved the EAC traces and determined the correlation time to be 300 as using the EAC of the ${{\rm{C}}^ +}$ channel. This is the shortest correlation time ever obtained in the autocorrelation measurements of APTs. The correlation times of the train envelopes for the respective fragment ions were in the range of 5.0–6.3 fs, showing that only a few attosecond pulses are included in the train. We have estimated the duration of an attosecond pulse within an APT to be 270 as by comparing the experimental results for the ${{\rm{H}}^ +}$ channel with the results of the simulation in which the spatial profile of the APT is taken into account, and we are now investigating the mechanism which makes the correlation times among the three fragment ion species different [38,48].

The FT spectra obtained from the IACs of the ${{\rm{C}}^ +}$ and ${{\rm{H}}^ +}$ channels were well reproduced by numerical simulations when the spatial profile of the APT is taken into account. We extracted the spectroscopic feature in the IAC trace of the ${{\rm{CH}}^ +}$ channel from the optical frequency components of the APT and found the enhancement of the yield at the seventh harmonic whose photon energy is about 11.0 eV. On the basis of the IAC traces of the experimental anisotropy parameter and the calculated transition dipole moments for the transitions from the electronic ground ${\tilde X^2}{\Pi _{\rm{u}}}$ state of ${{\rm{C}}_2}{\rm{H}}_2^ +$ to the electronically excited states, the increased yield of the ${{\rm{CH}}^ +}$ channel at the seventh harmonic was attributed to the resonant transition from the electronic ground ${\tilde X^2}{\Pi _{\rm{u}}}$ state of ${{\rm{C}}_2}{\rm{H}}_2^ +$ to the ${3^2}{\Pi _{\rm{g}}}$ state, leading to the formation of ${{\rm{CH}}^ +}$ through C–C bond breaking.

Although the IAC signals reflecting the temporal profile of APTs indicate that the dissociative ionization of ${{\rm{C}}_2}{{\rm{H}}_2}$ is a consequence of the ionization/excitation of ${{\rm{C}}_2}{{\rm{H}}_2}$ occurring within 300 as, we were able to successfully extract the evidence of a sequential process in which the ionization is followed by the resonant excitation. The combination analysis in time and spectral domains will provide us more information about the nonlinear phenomena induced by XUV photons.

Funding

Grants-in-Aid for Scientific Research, MEXT (18K05024, 20H00371, 19H05628, 26247068); Grant-in-Aid for Specially Promoted Research Grant, MEXT (JP15H05696); Core Research for Evolutional Science and Technology (JPMJCR15N1); Advanced Photon Science Alliance Research Project, MEXT; MEXT-Quantum Leap Flagship Program (JPMXS0118068681).

Acknowledgment

We thank Dr. T. Okino of RIKEN for his support in experiments and valuable discussions.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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References

  • View by:

  1. C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
    [Crossref]
  2. E. J. Takahashi, T. Kanai, and K. Midorikawa, “High-order harmonic generation by an ultrafast infrared pulse efficient generation of a coherent ‘water window’ x-ray,” Appl. Phys. B 100, 29–41 (2010).
    [Crossref]
  3. P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
    [Crossref]
  4. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
    [Crossref]
  5. P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, “Direct observation of attosecond light bunching,” Nature 426, 267–271 (2003).
    [Crossref]
  6. J. Van Tilborg, T. K. Allison, T. W. Wright, M. P. Hertlein, R. W. Falcone, Y. Liu, H. Merdji, and A. Belkacem, “Femtosecond isomerization dynamics in the ethylene cation measured in an EUV-pump NIR-probe configuration,” J. Phys. B 42, 081002 (2009).
    [Crossref]
  7. F. Kelkensberg, C. Lefebvre, W. Siu, O. Ghafur, T. T. Nguyen-Dang, O. Atabek, A. Keller, V. Serov, P. Johnsson, M. Swoboda, T. Remetter, A. L’Huillier, S. Zherebtsov, G. Sansone, E. Benedetti, F. Ferrari, M. Nisoli, F. Lépine, M. F. Kling, and M. J. J. Vrakking, “Molecular dissociative ionization and wave-packet dynamics studied using two-color XUV and IR pump-probe spectroscopy,” Phys. Rev. Lett. 103, 123005 (2009).
    [Crossref]
  8. T. K. Allison, H. Tao, W. J. Glover, T. W. Wright, A. M. Stooke, C. Khurmi, J. Van Tilborg, Y. Liu, R. W. Falcone, T. J. Martínez, and A. Belkacem, “Ultrafast internal conversion in ethylene. II. Mechanisms and pathways for quenching and hydrogen elimination,” J. Chem. Phys. 136, 124317 (2012).
    [Crossref]
  9. P. Ranitovic, C. W. Hogle, P. Rivière, A. Palacios, X.-M. Tong, N. Toshima, A. González-Castrillo, L. Martin, F. Martín, M. M. Murnane, and H. Kapteyn, “Attosecond vacuum UV coherent control of molecular dynamics,” Proc. Natl. Acad. Sci. USA 111, 912–917 (2014).
    [Crossref]
  10. R. Iikubo, T. Sekikawa, Y. Harabuchi, and T. Taketsugu, “Structural dynamics of photochemical reactions probed by time-resolved photoelectron spectroscopy using high harmonic pulses,” Faraday Discuss. 194, 147–160 (2016).
    [Crossref]
  11. Y. Nabekawa, Y. Furukawa, T. Okino, A. A. Eilanlou, E. J. Takahashi, K. Yamanouchi, and K. Midorikawa, “Sub-10-fs control of dissociation pathways in the hydrogen molecular ion with a few-pulse attosecond pulse train,” Nat. Commun. 7, 12835 (2016).
    [Crossref]
  12. V. Svoboda, N. B. Ram, R. Rajeev, and H. J. Wörner, “Time-resolved photoelectron imaging with a femtosecond vacuum-ultraviolet light source: dynamics in the$\tilde{A}/\tilde{B}$A~/B~- and$\tilde{F}$F~-bands of SO2,” J. Chem. Phys. 146, 084301 (2017).
    [Crossref]
  13. F. P. Sturm, X. M. Tong, A. Palacios, T. W. Wright, I. Zalyubovskaya, D. Ray, N. Shivaram, F. Martín, A. Belkacem, P. Ranitovic, and T. Weber, “Mapping and controlling ultrafast dynamics of highly excited H2 molecules by VUV-IR pump-probe schemes,” Phys. Rev. A 95, 012501 (2017).
    [Crossref]
  14. A. von Conta, A. Tehlar, A. Schletter, Y. Arasaki, K. Takatsuka, and H. J. Wörner, “Conical-intersection dynamics and ground-state chemistry probed by extreme-ultraviolet time-resolved photoelectron spectroscopy,” Nat. Commun. 9, 3162 (2018).
    [Crossref]
  15. E. Skantzakis, P. Tzallas, J. E. Kruse, C. Kalpouzos, O. Faucher, G. D. Tsakiris, and D. Charalambidis, “Tracking autoionizing-wave-packet dynamics at the 1-fs temporal scale,” Phys. Rev. Lett. 105, 043902 (2010).
    [Crossref]
  16. P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781–784 (2011).
    [Crossref]
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  18. T. Okino, Y. Furukawa, Y. Nabekawa, S. Miyabe, A. Amani Eilanlou, E. J. Takahashi, K. Yamanouchi, and K. Midorikawa, “Direct observation of an attosecond electron wave packet in a nitrogen molecule,” Sci. Adv. 1, a1500356 (2015).
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  22. M. Chini, S. Gilbertson, S. D. Khan, and Z. Chang, “Characterizing ultrabroadband attosecond lasers,” Opt. Express 18, 13006–13016 (2010).
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  24. Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime,” Phys. Rev. Lett. 97, 153904 (2006).
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  25. Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Conclusive evidence of an attosecond pulse train observed with the mode-resolved autocorrelation technique,” Phys. Rev. Lett. 96, 083901 (2006).
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  26. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605–608 (2004).
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  28. E. J. Takahashi, P. Lan, O. D. Mücke, Y. Nabekawa, and K. Midorikawa, “Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses,” Nat. Commun. 4, 2691 (2013).
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  29. Y. Nabekawa, A. Amani Eilanlou, Y. Furukawa, K. L. Ishikawa, H. Takahashi, and K. Midorikawa, “Multi-terawatt laser system generating 12-fs pulses at 100 Hz repetition rate,” Appl. Phys. B 101, 523–534 (2010).
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  30. E. Takahashi, Y. Nabekawa, and K. Midorikawa, “Generation of 10-µJ coherent extreme-ultraviolet light by use of high-order harmonics,” Opt. Lett. 27, 1920–1922 (2002).
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  32. D. Proch and T. Trickl, “A high-intensity multi-purpose piezoelectric pulsed molecular beam source,” Rev. Sci. Instrum. 60, 713–716 (1989).
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  33. Y. Ogi, H. Kohguchi, D. Niu, K. Ohshimo, and T. Suzuki, “Super-resolution photoelectron imaging with real-time subpixelation by field programmable gate array and its application to NO and benzene photoionization,” J. Phys. Chem. A 113, 14536–14544 (2009).
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  34. C. R. Gebhardt, T. P. Rakitzis, P. C. Samartzis, V. Ladopoulos, and T. N. Kitsopoulos, “Slice imaging: a new approach to ion imaging and velocity mapping,” Rev. Sci. Instrum. 72, 3848–3853 (2001).
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  35. T. Okino, K. Yamanouchi, T. Shimizu, K. Furusawa, H. Hasegawa, Y. Nabekawa, and K. Midorikawa, “Attosecond molecular coulomb explosion,” Chem. Phys. Lett. 432, 68–73 (2006).
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  36. T. Okino, K. Yamanouchi, T. Shimizu, R. Ma, Y. Nabekawa, and K. Midorikawa, “Attosecond nonlinear Fourier transformation spectroscopy of CO2 in extreme ultraviolet wavelength region,” J. Chem. Phys. 129, 161103 (2008).
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  37. T. Okino, Y. Furukawa, T. Shimizu, Y. Nabekawa, K. Yamanouchi, and K. Midorikawa, “Nonlinear Fourier transformation spectroscopy of small molecules with intense attosecond pulse train,” J. Phys. B 47, 124007 (2014).
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  38. Y. Nabekawa and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train calculated using feasible formulae,” New J. Phys. 10, 025034 (2008).
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  39. R. A. Mackie, S. W. J. Scully, A. M. Sands, R. Browning, K. F. Dunn, and C. J. Latimer, “A photoionization mass spectrometric study of acetylene and ethylene in the VUV spectral region,” Int. J. Mass Spectrom. 223-224, 67–79 (2003).
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  40. Y. H. Jiang, A. Rudenko, O. Herrwerth, L. Foucar, M. Kurka, K. U. Kühnel, M. Lezius, M. F. Kling, J. Van Tilborg, A. Belkacem, K. Ueda, S. Düsterer, R. Treusch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Ultrafast extreme ultraviolet induced isomerization of acetylene cations,” Phys. Rev. Lett. 105, 263002 (2010).
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  41. Y. H. Jiang, A. Senftleben, M. Kurka, A. Rudenko, L. Foucar, O. Herrwerth, M. F. Kling, M. Lezius, J. V. Tilborg, A. Belkacem, K. Ueda, D. Rolles, R. Treusch, Y. Z. Zhang, Y. F. Liu, C. D. Schröter, J. Ullrich, and R. Moshammer, “Ultrafast dynamics in acetylene clocked in a femtosecond XUV stopwatch,” J. Phys. B 46, 164027 (2013).
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  42. D. M. P. Holland, M. A. MacDonald, M. A. Hayes, L. Karlsson, and B. Wannberg, “A photoelectron spectroscopy study of the valence shell photoionization dynamics of acetylene,” J. Electron. Spectrosc. Relat. Phenom. 104, 245–255 (1999).
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  43. S. Svensson, E. Zdansky, U. Gelius, and H. Ågren, “High-energy x-ray-excited valence-electron photoemission spectroscopy of C2H2 and C2D2,” Phys. Rev. A 37, 4730–4733 (1988).
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  44. J. Pitarch-Ruiz, J. Sánchez-Marín, and D. Maynau, “Vertical spectrum of the C2H2+ system. An open shell (SC)2-CAS-SDCI study,” J. Comput. Chem. 24, 609–617 (2003).
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  45. M. Herman, A. Campargue, M. I. El Idrissi, and J. Vander Auwera, “Vibrational spectroscopic database on acetylene, X1∑g+ (12C2H2, 12C2D2, and 13C2H2),” J. Phys. Chem. Ref. Data 32, 921–929 (2003).
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  46. M. Davister and R. Locht, “The dissociative electroionization of C2H2, C2D2 and C2HD. Investigation of the [C2H(D)]+ and [H(D)]+ dissociation channels. The (D)H-C2H(D) binding energy,” Chem. Phys. 189, 805–824 (1994).
    [Crossref]
  47. M. Davister and R. Locht, “The dissociative ionization of C2H2 and C2D2. The [CH(CD)]+ dissociation channel. The H(D)C–C(D)H binding energy,” Chem. Phys. 191, 333–346 (1995).
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  48. M. Seel and W. Domcke, “Femtosecond time-resolved ionization spectroscopy of ultrafast internal-conversion dynamics in polyatomic molecules: theory and computational studies,” J. Chem. Phys. 95, 7806–7822 (1991).
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2018 (1)

A. von Conta, A. Tehlar, A. Schletter, Y. Arasaki, K. Takatsuka, and H. J. Wörner, “Conical-intersection dynamics and ground-state chemistry probed by extreme-ultraviolet time-resolved photoelectron spectroscopy,” Nat. Commun. 9, 3162 (2018).
[Crossref]

2017 (2)

V. Svoboda, N. B. Ram, R. Rajeev, and H. J. Wörner, “Time-resolved photoelectron imaging with a femtosecond vacuum-ultraviolet light source: dynamics in the$\tilde{A}/\tilde{B}$A~/B~- and$\tilde{F}$F~-bands of SO2,” J. Chem. Phys. 146, 084301 (2017).
[Crossref]

F. P. Sturm, X. M. Tong, A. Palacios, T. W. Wright, I. Zalyubovskaya, D. Ray, N. Shivaram, F. Martín, A. Belkacem, P. Ranitovic, and T. Weber, “Mapping and controlling ultrafast dynamics of highly excited H2 molecules by VUV-IR pump-probe schemes,” Phys. Rev. A 95, 012501 (2017).
[Crossref]

2016 (2)

R. Iikubo, T. Sekikawa, Y. Harabuchi, and T. Taketsugu, “Structural dynamics of photochemical reactions probed by time-resolved photoelectron spectroscopy using high harmonic pulses,” Faraday Discuss. 194, 147–160 (2016).
[Crossref]

Y. Nabekawa, Y. Furukawa, T. Okino, A. A. Eilanlou, E. J. Takahashi, K. Yamanouchi, and K. Midorikawa, “Sub-10-fs control of dissociation pathways in the hydrogen molecular ion with a few-pulse attosecond pulse train,” Nat. Commun. 7, 12835 (2016).
[Crossref]

2015 (2)

Y. Nabekawa, Y. Furukawa, T. Okino, A. Amani Eilanlou, E. J. Takahashi, K. Yamanouchi, and K. Midorikawa, “Settling time of a vibrational wavepacket in ionization,” Nat. Commun. 6, 8197 (2015).
[Crossref]

T. Okino, Y. Furukawa, Y. Nabekawa, S. Miyabe, A. Amani Eilanlou, E. J. Takahashi, K. Yamanouchi, and K. Midorikawa, “Direct observation of an attosecond electron wave packet in a nitrogen molecule,” Sci. Adv. 1, a1500356 (2015).
[Crossref]

2014 (2)

P. Ranitovic, C. W. Hogle, P. Rivière, A. Palacios, X.-M. Tong, N. Toshima, A. González-Castrillo, L. Martin, F. Martín, M. M. Murnane, and H. Kapteyn, “Attosecond vacuum UV coherent control of molecular dynamics,” Proc. Natl. Acad. Sci. USA 111, 912–917 (2014).
[Crossref]

T. Okino, Y. Furukawa, T. Shimizu, Y. Nabekawa, K. Yamanouchi, and K. Midorikawa, “Nonlinear Fourier transformation spectroscopy of small molecules with intense attosecond pulse train,” J. Phys. B 47, 124007 (2014).
[Crossref]

2013 (2)

Y. H. Jiang, A. Senftleben, M. Kurka, A. Rudenko, L. Foucar, O. Herrwerth, M. F. Kling, M. Lezius, J. V. Tilborg, A. Belkacem, K. Ueda, D. Rolles, R. Treusch, Y. Z. Zhang, Y. F. Liu, C. D. Schröter, J. Ullrich, and R. Moshammer, “Ultrafast dynamics in acetylene clocked in a femtosecond XUV stopwatch,” J. Phys. B 46, 164027 (2013).
[Crossref]

E. J. Takahashi, P. Lan, O. D. Mücke, Y. Nabekawa, and K. Midorikawa, “Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses,” Nat. Commun. 4, 2691 (2013).
[Crossref]

2012 (1)

T. K. Allison, H. Tao, W. J. Glover, T. W. Wright, A. M. Stooke, C. Khurmi, J. Van Tilborg, Y. Liu, R. W. Falcone, T. J. Martínez, and A. Belkacem, “Ultrafast internal conversion in ethylene. II. Mechanisms and pathways for quenching and hydrogen elimination,” J. Chem. Phys. 136, 124317 (2012).
[Crossref]

2011 (1)

P. Tzallas, E. Skantzakis, L. A. A. Nikolopoulos, G. D. Tsakiris, and D. Charalambidis, “Extreme-ultraviolet pump-probe studies of one-femtosecond-scale electron dynamics,” Nat. Phys. 7, 781–784 (2011).
[Crossref]

2010 (5)

E. Skantzakis, P. Tzallas, J. E. Kruse, C. Kalpouzos, O. Faucher, G. D. Tsakiris, and D. Charalambidis, “Tracking autoionizing-wave-packet dynamics at the 1-fs temporal scale,” Phys. Rev. Lett. 105, 043902 (2010).
[Crossref]

E. J. Takahashi, T. Kanai, and K. Midorikawa, “High-order harmonic generation by an ultrafast infrared pulse efficient generation of a coherent ‘water window’ x-ray,” Appl. Phys. B 100, 29–41 (2010).
[Crossref]

Y. Nabekawa, A. Amani Eilanlou, Y. Furukawa, K. L. Ishikawa, H. Takahashi, and K. Midorikawa, “Multi-terawatt laser system generating 12-fs pulses at 100 Hz repetition rate,” Appl. Phys. B 101, 523–534 (2010).
[Crossref]

M. Chini, S. Gilbertson, S. D. Khan, and Z. Chang, “Characterizing ultrabroadband attosecond lasers,” Opt. Express 18, 13006–13016 (2010).
[Crossref]

Y. H. Jiang, A. Rudenko, O. Herrwerth, L. Foucar, M. Kurka, K. U. Kühnel, M. Lezius, M. F. Kling, J. Van Tilborg, A. Belkacem, K. Ueda, S. Düsterer, R. Treusch, C. D. Schröter, R. Moshammer, and J. Ullrich, “Ultrafast extreme ultraviolet induced isomerization of acetylene cations,” Phys. Rev. Lett. 105, 263002 (2010).
[Crossref]

2009 (3)

Y. Ogi, H. Kohguchi, D. Niu, K. Ohshimo, and T. Suzuki, “Super-resolution photoelectron imaging with real-time subpixelation by field programmable gate array and its application to NO and benzene photoionization,” J. Phys. Chem. A 113, 14536–14544 (2009).
[Crossref]

J. Van Tilborg, T. K. Allison, T. W. Wright, M. P. Hertlein, R. W. Falcone, Y. Liu, H. Merdji, and A. Belkacem, “Femtosecond isomerization dynamics in the ethylene cation measured in an EUV-pump NIR-probe configuration,” J. Phys. B 42, 081002 (2009).
[Crossref]

F. Kelkensberg, C. Lefebvre, W. Siu, O. Ghafur, T. T. Nguyen-Dang, O. Atabek, A. Keller, V. Serov, P. Johnsson, M. Swoboda, T. Remetter, A. L’Huillier, S. Zherebtsov, G. Sansone, E. Benedetti, F. Ferrari, M. Nisoli, F. Lépine, M. F. Kling, and M. J. J. Vrakking, “Molecular dissociative ionization and wave-packet dynamics studied using two-color XUV and IR pump-probe spectroscopy,” Phys. Rev. Lett. 103, 123005 (2009).
[Crossref]

2008 (3)

J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92, 25–32 (2008).
[Crossref]

T. Okino, K. Yamanouchi, T. Shimizu, R. Ma, Y. Nabekawa, and K. Midorikawa, “Attosecond nonlinear Fourier transformation spectroscopy of CO2 in extreme ultraviolet wavelength region,” J. Chem. Phys. 129, 161103 (2008).
[Crossref]

Y. Nabekawa and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train calculated using feasible formulae,” New J. Phys. 10, 025034 (2008).
[Crossref]

2006 (4)

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime,” Phys. Rev. Lett. 97, 153904 (2006).
[Crossref]

Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Conclusive evidence of an attosecond pulse train observed with the mode-resolved autocorrelation technique,” Phys. Rev. Lett. 96, 083901 (2006).
[Crossref]

A. Kosuge, T. Sekikawa, X. Zhou, T. Kanai, S. Adachi, and S. Watanabe, “Frequency-resolved optical gating of isolated attosecond pulses in the extreme ultraviolet,” Phys. Rev. Lett. 97, 263901 (2006).
[Crossref]

T. Okino, K. Yamanouchi, T. Shimizu, K. Furusawa, H. Hasegawa, Y. Nabekawa, and K. Midorikawa, “Attosecond molecular coulomb explosion,” Chem. Phys. Lett. 432, 68–73 (2006).
[Crossref]

2005 (1)

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Phys. Rev. A 71, 011401 (2005).
[Crossref]

2004 (1)

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605–608 (2004).
[Crossref]

2003 (5)

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003).
[Crossref]

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, “Direct observation of attosecond light bunching,” Nature 426, 267–271 (2003).
[Crossref]

R. A. Mackie, S. W. J. Scully, A. M. Sands, R. Browning, K. F. Dunn, and C. J. Latimer, “A photoionization mass spectrometric study of acetylene and ethylene in the VUV spectral region,” Int. J. Mass Spectrom. 223-224, 67–79 (2003).
[Crossref]

J. Pitarch-Ruiz, J. Sánchez-Marín, and D. Maynau, “Vertical spectrum of the C2H2+ system. An open shell (SC)2-CAS-SDCI study,” J. Comput. Chem. 24, 609–617 (2003).
[Crossref]

M. Herman, A. Campargue, M. I. El Idrissi, and J. Vander Auwera, “Vibrational spectroscopic database on acetylene, X1∑g+ (12C2H2, 12C2D2, and 13C2H2),” J. Phys. Chem. Ref. Data 32, 921–929 (2003).
[Crossref]

2002 (1)

2001 (2)

C. R. Gebhardt, T. P. Rakitzis, P. C. Samartzis, V. Ladopoulos, and T. N. Kitsopoulos, “Slice imaging: a new approach to ion imaging and velocity mapping,” Rev. Sci. Instrum. 72, 3848–3853 (2001).
[Crossref]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

1999 (1)

D. M. P. Holland, M. A. MacDonald, M. A. Hayes, L. Karlsson, and B. Wannberg, “A photoelectron spectroscopy study of the valence shell photoionization dynamics of acetylene,” J. Electron. Spectrosc. Relat. Phenom. 104, 245–255 (1999).
[Crossref]

1998 (1)

1997 (2)

A. T. J. B. Eppink and D. H. Parker, “Velocity map imaging of ions and electrons using electrostatic lenses: application in photoelectron and photofragment ion imaging of molecular oxygen,” Rev. Sci. Instrum. 68, 3477–3484 (1997).
[Crossref]

C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

1996 (1)

P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[Crossref]

1995 (1)

M. Davister and R. Locht, “The dissociative ionization of C2H2 and C2D2. The [CH(CD)]+ dissociation channel. The H(D)C–C(D)H binding energy,” Chem. Phys. 191, 333–346 (1995).
[Crossref]

1994 (1)

M. Davister and R. Locht, “The dissociative electroionization of C2H2, C2D2 and C2HD. Investigation of the [C2H(D)]+ and [H(D)]+ dissociation channels. The (D)H-C2H(D) binding energy,” Chem. Phys. 189, 805–824 (1994).
[Crossref]

1991 (1)

M. Seel and W. Domcke, “Femtosecond time-resolved ionization spectroscopy of ultrafast internal-conversion dynamics in polyatomic molecules: theory and computational studies,” J. Chem. Phys. 95, 7806–7822 (1991).
[Crossref]

1989 (1)

D. Proch and T. Trickl, “A high-intensity multi-purpose piezoelectric pulsed molecular beam source,” Rev. Sci. Instrum. 60, 713–716 (1989).
[Crossref]

1988 (1)

S. Svensson, E. Zdansky, U. Gelius, and H. Ågren, “High-energy x-ray-excited valence-electron photoemission spectroscopy of C2H2 and C2D2,” Phys. Rev. A 37, 4730–4733 (1988).
[Crossref]

Adachi, S.

A. Kosuge, T. Sekikawa, X. Zhou, T. Kanai, S. Adachi, and S. Watanabe, “Frequency-resolved optical gating of isolated attosecond pulses in the extreme ultraviolet,” Phys. Rev. Lett. 97, 263901 (2006).
[Crossref]

Agostini, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302, 1540–1543 (2003).
[Crossref]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Ågren, H.

S. Svensson, E. Zdansky, U. Gelius, and H. Ågren, “High-energy x-ray-excited valence-electron photoemission spectroscopy of C2H2 and C2D2,” Phys. Rev. A 37, 4730–4733 (1988).
[Crossref]

Allison, T. K.

T. K. Allison, H. Tao, W. J. Glover, T. W. Wright, A. M. Stooke, C. Khurmi, J. Van Tilborg, Y. Liu, R. W. Falcone, T. J. Martínez, and A. Belkacem, “Ultrafast internal conversion in ethylene. II. Mechanisms and pathways for quenching and hydrogen elimination,” J. Chem. Phys. 136, 124317 (2012).
[Crossref]

J. Van Tilborg, T. K. Allison, T. W. Wright, M. P. Hertlein, R. W. Falcone, Y. Liu, H. Merdji, and A. Belkacem, “Femtosecond isomerization dynamics in the ethylene cation measured in an EUV-pump NIR-probe configuration,” J. Phys. B 42, 081002 (2009).
[Crossref]

Amani Eilanlou, A.

Y. Nabekawa, Y. Furukawa, T. Okino, A. Amani Eilanlou, E. J. Takahashi, K. Yamanouchi, and K. Midorikawa, “Settling time of a vibrational wavepacket in ionization,” Nat. Commun. 6, 8197 (2015).
[Crossref]

T. Okino, Y. Furukawa, Y. Nabekawa, S. Miyabe, A. Amani Eilanlou, E. J. Takahashi, K. Yamanouchi, and K. Midorikawa, “Direct observation of an attosecond electron wave packet in a nitrogen molecule,” Sci. Adv. 1, a1500356 (2015).
[Crossref]

Y. Nabekawa, A. Amani Eilanlou, Y. Furukawa, K. L. Ishikawa, H. Takahashi, and K. Midorikawa, “Multi-terawatt laser system generating 12-fs pulses at 100 Hz repetition rate,” Appl. Phys. B 101, 523–534 (2010).
[Crossref]

Antoine, P.

P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics,” Phys. Rev. Lett. 77, 1234–1237 (1996).
[Crossref]

Arasaki, Y.

A. von Conta, A. Tehlar, A. Schletter, Y. Arasaki, K. Takatsuka, and H. J. Wörner, “Conical-intersection dynamics and ground-state chemistry probed by extreme-ultraviolet time-resolved photoelectron spectroscopy,” Nat. Commun. 9, 3162 (2018).
[Crossref]

Atabek, O.

F. Kelkensberg, C. Lefebvre, W. Siu, O. Ghafur, T. T. Nguyen-Dang, O. Atabek, A. Keller, V. Serov, P. Johnsson, M. Swoboda, T. Remetter, A. L’Huillier, S. Zherebtsov, G. Sansone, E. Benedetti, F. Ferrari, M. Nisoli, F. Lépine, M. F. Kling, and M. J. J. Vrakking, “Molecular dissociative ionization and wave-packet dynamics studied using two-color XUV and IR pump-probe spectroscopy,” Phys. Rev. Lett. 103, 123005 (2009).
[Crossref]

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Balcou, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Belkacem, A.

F. P. Sturm, X. M. Tong, A. Palacios, T. W. Wright, I. Zalyubovskaya, D. Ray, N. Shivaram, F. Martín, A. Belkacem, P. Ranitovic, and T. Weber, “Mapping and controlling ultrafast dynamics of highly excited H2 molecules by VUV-IR pump-probe schemes,” Phys. Rev. A 95, 012501 (2017).
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Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1. Spectral fluence of an APT at the focus estimated from the HH spectrum and the fundamental and third-harmonic spectra.
Fig. 2.
Fig. 2. (a) Delay-dependent signal intensities of ${{\rm{CH}}^ +}$ (left), ${{\rm{C}}^ +}$ (center), and ${{\rm{H}}^ +}$ (right) fragments. The signals of ${{\rm{CH}}^ +}$ and ${{\rm{C}}^ +}$ are obtained by integrating their yields in the kinetic energy range below 5 eV. The signal of ${{\rm{H}}^ +}$ is obtained by integrating its yield in the kinetic energy range below 8 eV. (b) Envelope autocorrelation traces of APTs in the three channels. The bandpass filter extracting even-order harmonic components from 0th to 8th is applied to the respective interferometric autocorrelation traces. Black dashed lines show the baselines. An error bar in each panel in (a) and (b) was evaluated by assuming the Poisson statistics of the number of ion fragments counted. We plot one representative error bar in each trace so that the trace will not be covered by many error bars. The error bar for each delay step was deviated only 20% at most from the representative error bar.
Fig. 3.
Fig. 3. Correlation time (${T_{{\rm{pulse}}}}$) defined as the FWHM of the central peak in the EAC trace calculated as a function of GDD. The correlation times obtained using different two-photon energy thresholds (${E_{{\rm{th}}}}$) are plotted in black (${E_{{\rm{th}}}} = 0$ eV), green (${E_{{\rm{th}}}} = 18.9$ eV), blue (${E_{{\rm{th}}}} = 21.4$ eV), and red (${E_{{\rm{th}}}} = 24.8$ eV). Dotted curves: ${T_{{\rm{pulse}}}}$ obtained without considering the spatial profile. The color codes for the two-photon energy threshold are the same as those for the circles. The correlation times obtained from the experimental autocorrelation traces for the ${{\rm{C}}^ +}$, ${{\rm{CH}}^ +}$, and ${{\rm{H}}^ +}$ channels are indicated as starting points of the horizontal dotted red, blue, and green arrows, respectively. The vertical dotted arrows indicate the corresponding GDD values.
Fig. 4.
Fig. 4. FT spectra of the IAC traces obtained for the ${{\rm{CH}}^ +}$ (blue), ${{\rm{C}}^ +}$ (red), and ${{\rm{H}}^ +}$ (green) channels, which are scaled so that the integrated areas in the range between 1 and 25 eV become the same.
Fig. 5.
Fig. 5. (a) Bottom panel: The FT spectrum of the IAC trace for ${{\rm{C}}^ +}$ channel, which is the same as that shown in the middle panel of Fig. 4, is depicted as a red shaded area. The FT spectra of the IAC traces obtained by model calculations with and without considering the spatial profiles of the APT are depicted as purple and orange solid curves, respectively. Upper panel: experimental peak areas of the respective harmonic components for the ${{\rm{C}}^ +}$ channel (red shaded area) are plotted with red circles. The peak areas obtained by model calculation in which the spatial profiles of the APT are taken into account (purple circles) and those obtained by neglecting the spatial profiles of APT (orange circles) are also shown. The FT spectra are calculated with the GDD value of $1.0 \times {10^{- 32}}\; {{\rm{s}}^2}$ and the threshold energy of 24.8 eV. (b) Peak areas of the respective harmonic components relative to those obtained by model calculations. The scaled peak areas for the ${{\rm{CH}}^ +}$, ${{\rm{C}}^ +}$, and ${{\rm{H}}^ +}$ channels are shown with blue solid triangles, red solid circles, and green solid squares, respectively.
Fig. 6.
Fig. 6. Real parts of the Fourier transform spectra of the anisotropy parameter obtained for the ${{\rm{CH}}^ +}$ (left), ${{\rm{C}}^ +}$ (center), and ${{\rm{H}}^ +}$ (right) channels. The anisotropy parameters of the ${{\rm{CH}}^ +}$ and ${{\rm{C}}^ +}$ channels are obtained by integrating the fragment yields at kinetic energies below 1.5 eV and the anisotropy parameter of ${{\rm{H}}^ +}$ channel is obtained by integrating the fragment yield at kinetic energies below 3 eV.
Fig. 7.
Fig. 7. Theoretical potential energy curves of the low-lying electronic states of ${{\rm{C}}_2}{\rm{H}}_2^ +$ along the C–C internuclear distance $r({\rm{CC}})$. The two ${\rm{C}} - {\rm{H}}$ internuclear distances are fixed to be 1.061 Å. The gray vertical line represents the equilibrium C–C internuclear distance of neutral ${{\rm{C}}_2}{{\rm{H}}_2}$ at 1.203 Å. The gray shaded curve represents the probability distribution of the C–C internuclear distance of the vibrational ground level of the electronic ground state of neutral ${{\rm{C}}_2}{{\rm{H}}_2}$. The energy is the relative value with respect to that of the ${1^2}{\Pi _{\rm{u}}}$ state at 1.203 Å. Open circles represent the potential energies reported by Pitarch-Ruiz et al. [44] at $r({\rm{CH}}) = 1.061 $ Å and $r({\rm{CC}}) = 1.203 $ Å. The short horizontal bars on the right side of the figure represent the three lowest dissociation limits of ${{\rm{C}}_2}{\rm{H}}_2^ +$ [46,47].

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