The Multielectron Ionization Dynamics Underlying Attosecond Strong-Field Spectroscopies

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Science  16 Mar 2012:
Vol. 335, Issue 6074, pp. 1336-1340
DOI: 10.1126/science.1212896


Subcycle strong-field ionization (SFI) underlies many emerging spectroscopic probes of atomic or molecular attosecond electronic dynamics. Extending methods such as attosecond high harmonic generation spectroscopy to complex polyatomic molecules requires an understanding of multielectronic excitations, already hinted at by theoretical modeling of experiments on atoms, diatomics, and triatomics. Here, we present a direct method which, independent of theory, experimentally probes the participation of multiple electronic continua in the SFI dynamics of polyatomic molecules. We use saturated (n-butane) and unsaturated (1,3-butadiene) linear hydrocarbons to show how subcycle SFI of polyatomics can be directly resolved into its distinct electronic-continuum channels by above-threshold ionization photoelectron spectroscopy. Our approach makes use of photoelectron-photofragment coincidences, suiting broad classes of polyatomic molecules.

To date, measurements of attosecond electronic dynamics in atoms and molecules (1) have typically involved strong laser-field processes. Even pump-probe spectroscopies using isolated attosecond pulses rely on the presence of a phased, strong (~1013 W/cm2) laser field (24). The process of high harmonic generation (HHG), which can probe electronic wave packets on attosecond time scales (59), is entirely based on strong-field ionization (SFI), as is the use of subcycle electron recollision for probing dynamics (10, 11). In the interpretation of experiments, broad use is made of the three-step model (12) wherein SFI adiabatically releases, via tunneling, a single continuum electron that is subsequently driven in the strong, oscillating laser field. However, even in simple diatomics, the possible role of multiple electronic continua in attosecond SFI measurements (5, 13, 14) is unclear (6, 15). In the complex world of multielectron polyatomic molecules, adiabatic single-electron tunneling approximations are very unlikely to hold (1619). Nevertheless, to have broader impact, attosecond HHG spectroscopies must be extended to polyatomic molecules (20), and therefore, a general understanding of the role of multielectron SFI dynamics in polyatomics is required. Here, we introduce the channel-resolved above-threshold ionization (CRATI) method, where the channel refers to the electronic state of the ion correlated with the continuum electron. Independent of theoretical models, we experimentally resolve the multiple electronic continuum channels in SFI of polyatomic systems. By studying the CRATI of the linear hydrocarbons 1,3-butadiene and n-butane, we unambiguously demonstrate the direct, subcycle participation of multiple final ionic states in molecular SFI. We show that the population of higher-lying electronic continua can, depending on molecular properties, even exceed that of the ground state. We independently corroborate our experimental results with high-level, all-electron dynamical Schrödinger equation calculations. These combined results show that the relative contributions of these multiple continuum channels depend on both molecular electronic structure and laser-field properties and that both adiabatic and nonadiabatic laser-driven electronic dynamics may result.

A seminal attosecond transient absorption spectroscopy study recently demonstrated the coherent population (amplitudes and phases) of spin-orbit states due to SFI of krypton atoms (2). This technique benefitted from the presence of sharp features in the absorption spectrum that identified the two coherently prepared ionic states. To discern the ionic states of polyatomic molecules populated by SFI, alternate approaches might be required, because transient absorption spectroscopy of polyatomics is much more complex. Our experimental approach is based on above-threshold ionization (ATI) (2124), a universal SFI phenomenon wherein a field-driven continuum electron absorbs excess photons beyond the minimum number required for ionization. This leads to observation of a series of peaks in the electron kinetic energy spectrum, spaced by the photon energy. There is a deep connection between ATI and the process of HHG. In both cases, subcycle SFI generates a continuum electron that, depending on phase, either recollides with its ion core and emits a burst of extreme ultraviolet radiation (HHG) or accelerates away from the ion as an energetic electron (ATI). In either case, a single-cycle pulse would result in structureless HHG and ATI spectra. Structured spectra arise from this subcycle emission (photon or electron) being repeated every optical cycle. First evidence for the participation of multiple continua in HHG spectroscopy of molecules emerged from experiments on CO2 (5, 25), N2 (6, 26, 27), and N2O4 (28), each relying strongly on theoretical modeling for interpretation. These results caution that essential multiple continuum effects should not be ignored. Such effects are to be expected in the SFI of polyatomic molecules, because their many valence electrons should all respond to the strong laser electric field. We find, for the molecules studied here, that electrons can be ejected by tunneling via independent channels, populating the ionic ground state [ejection of the highest occupied molecular orbital (HOMO) electron; i.e., HOMO ionization] and/or excited (for instance, HOMO–1 ionization) electronic states. By independent, we mean that the continuum channels remain uncoupled (that is, no transitions between them) in the laser field. However, in other molecular systems and/or at higher laser intensity, nonadiabatic interchannel coupling can occur during SFI. In this situation, another bound electron makes a laser-induced transition on a subcycle time scale as the continuum electron departs. This process is termed nonadiabatic multielectron (NME) ionization (16) and will be discussed below. Whether the response is adiabatic or not, population of multiple electronic continua will be a generic feature of SFI of polyatomic molecules. To distinguish SFI channels populating the ionic ground-state continuum from those populating ionic excited-state continua, we make use of the fact that, unlike diatomics, electronically excited polyatomic ions generally undergo rapid radiationless transitions, which leads to fragmentation (29, 30). This is the case for the linear hydrocarbons studied here, 1,3-butadiene (C4H6) and n-butane (C4H10): Only their ionic electronic ground state is stable, whereas transitions to electronically excited ionic states lead to unimolecular dissociation of the parent ion, producing fragments on a time scale much longer than the laser interaction (3133). However, in a strong laser field, fragment ions may also be produced by postionization excitation of the ionic ground state. Therefore, the observation of ionic fragmentation in itself does not constitute proof that the SFI process directly populates electronically excited ionic states. Experimentally, we need to distinguish two SFI pathways: (i) subcycle ionization directly into an ionic excited state versus (ii) ionization forming the ionic ground state, followed by subsequent excitation during the laser cycles after ionization. In our CRATI experiment, this is achieved by measuring the ATI kinetic energy spectrum in coincidence (or covariance) with parent and fragment ions. As described in the supporting online material (SOM), the covariance-mapping method reveals correlations between ions and electrons via statistical analysis of count-rate fluctuations (34). The ATI spectrum consists of a comb of electron kinetic energies spaced by the photon energy (Eq. 1)E=mω[IP(Dj)UP] (1)where m is an integer and ħω is the photon energy. For the molecular core, IP(Dj) is the Stark-shifted molecular ionization potential of the jth ionization channel (where j = 0 signifies the D0 ground electronic state of the ion, j =1 the D1 first excited electronic state of the ion, and so forth) and accounts for the relative Stark shifts of both neutral and ionic states. UP is the ponderomotive (quiver) energy of a free electron (charge e, mass me) in an oscillating laser field of angular frequency ω and electric field amplitude E0 (Eq. 2)

UP = e2E024meω2  (2)

As described in detail in the SOM, the Stark-shifted ionization potential IP(Dj) is the field-free ionization potential plus the difference in Stark shift between the neutral ground state and the jth ionization channel. Due to their differing IP(Dj), the different ionization channels will have ATI combs shifted with respect to each other. If direct SFI to an electronically excited ion state Dj occurs, the correlated ion fragments will exhibit an ATI comb shifted relative to that correlated with the parent ion. In contrast, if ion excited states were populated subsequently by postionization excitation, meaning that the continuum electron has departed before further excitation occurs, then the fragments would have the same ATI spectrum as the parent ion because postionization excitation can no longer influence the departed continuum electron. Note that whereas several electronically excited ionization channels might correlate with the same ion fragment, the parent ion will uniquely identify the D0 ground-state ionization channel. By our method, we can determine whether SFI directly produced ionic ground or excited states, or whether ionic excited states were sequentially populated after removal of the electron. In Table 1 and table S1, we list the vertical and Stark-shifted ionization potentials IP(Dj) of the lowest four ionic electronic states for the molecules studied here. As seen from Eqs. 1 and 2, the ATI shift depends on laser intensity and, therefore, spatial averaging over the laser focal volume reduces the contrast of the ATI peaks. As discussed in the SOM, we explicitly minimized this effect by using a restricted target volume geometry. We obtained absolute intensity calibrations by studying the shift of the ATI combs with laser intensity (i.e., UP) for the H2O molecule, in which the molecular Stark shifts are negligible. In our measurements, the value of UP in Eq. 1 is very similar for all participating ionic states. This is because, for the low count-rate requirements of our covariance experiment, ionization is spatially restricted to the very center of the laser focus. In SFI, possible excited-state resonances in the neutral molecule can produce the well-known Freeman resonances (35), leading to sharp features in the ATI spectra, which have a limited progression. We indeed observed Freeman resonances in these molecular systems (see fig. S2 and accompanying text), as confirmed by their laser-intensity independence. In contrast, the ATI peaks shift monotonically with laser intensity. In low-frequency fields, the Freeman resonances contribute only to the first two or three ATI peaks: The shifts reported here are based on the higher members of the ATI progression. Therefore, the possible excitation of neutral excited states does not affect our analysis of the ATI comb shifts. By studying CRATI as a function of the ellipticity of the driving field, we furthermore confirmed that electron recollision played no important role in producing excited states.

Table 1

Vertical field-free ionization potentials Embedded Image and Stark-shifted ionization potentials Embedded Image (in electron volts) of the first four ionic states (Dj, j = 0 to 3) of n-butane and three ionic states (Dj, j =0, 1, 2) of 1,3-butadiene. The Embedded Image are measured values taken from (38) unless otherwise indicated. Embedded Image values include the calculated Stark shift of the jth ionization potential, as described in the SOM. As the CRATI measurements were performed in presence of the laser field, the Embedded Image values pertain for comparison with experiment.

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The details of the experimental geometry, data collection, and analysis are presented in the SOM. In Fig. 1, we present the mass spectrum (left) and normalized CRATI photoelectron spectra (right) for 1,3-butadiene at a peak intensity of 1.9 × 1013 W/cm2 (ħω = 798 nm/1.55 eV, UP = 1.16 eV). The mass spectrum is strongly dominated by the parent ion C4H6+, which accounts for 87% of the overall ion yield. This number directly gives a lower limit for the probability of formation of the D0 ionic ground electronic state in SFI of 1,3-butadiene, corresponding to HOMO ionization. A small (13%) contribution from fragments is also seen in the mass spectrum, indicating population of ionic excited states. As a percent ratio of the parent ion signal, the most prominent fragmentation channels are C4H5+ (1%), C3H3+ (3%), and C2H3+ (3%). The CRATI photoelectron spectra (right) show a series of peaks spaced by the photon energy, as expected. The CRATI peaks correlated with the parent C4H6+ ion yield a comb associated with ionization into the X(D0) ground state. In Fig. 1B, the vertical lines indicate the relative shift of the ATI combs, determined from analysis of the higher-order peaks contributing to each comb. Relative to the C4H6+ comb, the CRATI combs of the C4H5+ and C3H3+ fragment channels are both shifted toward lower energy by 0.95 ± 0.05 eV, as determined by statistical analysis of the relative comb shifts. This is unambiguous experimental evidence of direct SFI into ion excited states in 1,3-butadiene: Postionization fragmentation of the D0 ground state could not produce this result. From Table 1, the Stark-shifted D1(2Au) and D2(2Ag) states of the 1,3-butadiene ion lie 2.3 and 2.5 eV above the Stark-shifted D0(2Bg) ground state, respectively. The ATI comb shift can only be observed modulo the photon energy (1.55 eV). Therefore, direct SFI to the D1(2Au)/D2(2Ag) states should produce an average CRATI comb shifted relative to that of the ground state by 2.40 – 1.55 = 0.85 eV. Within errors, this is quantitatively the shift observed for the C4H5+ and C3H3+ CRATI combs. This conclusion is further supported by prior tunable vacuum ultraviolet single-photon ionization studies on 1,3-butadiene, which showed that the C4H5+ and C3H3+ fragments appear as soon as the D1(2Au) ion state is energetically accessible (32). In contrast, the C2H3+ fragment has an appearance energy more than 6 eV above that of the parent ion (32). In our experiment, C2H3+ probably originates from further excitation of the ion in subsequent field cycles. As can be seen in Fig. 1B, the C2H3+ CRATI spectrum exhibits fairly washed out ATI structure with little modulation depth, consistent with several SFI channels contributing to the formation of this fragment. We can rule out the population of neutral excited states within the laser pulse, leading to their SFI and associated ATI comb: This is not consistent with the present results because the lower IP (which determines their ATI comb shift) of a neutral excited state does not match those due to ionization of the neutral ground state.

Fig. 1

Strong-field ionization of 1,3-butadiene at a peak intensity of 1.9 × 1013 W/cm2. (A) Mass spectrum with the most prominent peak being the parent C4H6+ ion. Fragment ions C4H5+, C3H3+, and C2H3+ that originate from the unstable D1 excited ion state were also observed. amu, atomic mass units. (B) CRATI photoelectron spectra correlated with both parent and fragment ions. As indicated by the vertical lines, the fragment CRATI combs are shifted in energy relative to that of the parent ion (black) by 0.95 ± 0.05 eV. This is quantitatively the energy difference between the Stark-shifted D0 and D1 ionic states in 1,3-butadiene, modulo the photon energy, which unambiguously demonstrates that the excited D1 ion state was directly populated from the neutral ground state. For a detailed discussion, see the text.

In Fig. 2, we present mass (left) and CRATI spectra (right) for n-butane at a peak intensity of 1.6 × 1013 W/cm2 (ħω = 798 nm/1.55 eV, UP = 0.93 eV). In contrast to 1,3-butadiene, n-butane predominantly fragments upon ionization, producing C3Hn+ and C2Hn+ ions. The C3H7+ and C3H6+ fragments are associated with populating the first ionic excited state, whereas the C2H5+ fragment is known to be associated with the third ionic excited state (33). Relative to the parent ion signal, the percent ratio of the fragment ions are: C3H7+ (122%), C3H6+ (27%), C2H5+ (96%), and C2H3+ (152%). Figure 2B shows that the C3H7+ fragment CRATI comb (blue) is shifted to lower energy by 0.45 ± 0.05 eV relative to the parent ion comb (black). As seen in Table 1, the energy difference between the Stark-shifted D0 ion ground state and the field-split D1(2Bg)/D2(2Ag) ionic excited states of n-butane is 0.4/0.5 eV, in quantitative agreement with the shift of the C3H7+ comb (blue) in Fig. 2B. This reveals that the dominant C3H7+ channel is due to direct SFI into the first excited ionic state. Figure 2B also shows that the C3H6+ CRATI comb (red) is shifted to lower energy by 0.40 ± 0.05 eV relative to the parent ion comb. Therefore, within experimental error, we can also associate C3H6+ with direct SFI into the first ion excited state. The C2H5+ (green) and C2H3+ (see SOM) fragment combs are both shifted to lower energy by 0.10 ± 0.05 eV relative to the parent ion comb. Although this shift is not in strict quantitative agreement with the data given in Table 1, within the approximations used in calculating the excited-state polarizabilities, it is consistent with direct SFI into the third ion excited state. The CRATI results for n-butane show that SFI to electronically excited continuum channels can dominate over SFI to the ground state. In sum, the combined results of Figs. 1 and 2 experimentally demonstrate that multiple continua do participate in the direct SFI of polyatomic molecules, with the relative contributions of these channels depending on molecular electronic structure. In the following, we interpret these observations in terms of the attosecond molecular SFI response.

Fig. 2

Strong-field ionization of n-butane at a peak intensity of 1.6 × 1013 W/cm2. (A) Mass spectrum. (B) CRATI photoelectron spectra correlated with different fragment ions. Extensive fragmentation occurs even at low intensity. Several fragment CRATI combs show a shift relative to that of the parent ion (black). These can be quantitatively assigned to originate from direct SFI into excited ionic states.

The experimental results are independently (that is, using no adjustable parameters) corroborated by all-electron, coupled-channel time-dependent Schrödinger equation (TDSE) calculations, which are outlined in detail in the SOM. Briefly, this mixed orbital/grid-based approach (36) makes no assumptions about the nature of the ionization mechanism or the adiabaticity of the field-driven electron response. The neutral ground state and the ground and excited ionic states are treated at an appropriate level of ab initio electronic structure theory. Both the bound electrons and the continuum electron are treated in the full three spatial dimensions, whereas the nuclei are kept frozen at the ground-state neutral geometry. The only central approximations are that: (i) a finite number of final ion electronic states are included (seven for 1,3-butadiene, eight for n-butane), and (ii) upon excitation, the departing electron is no longer antisymmetrized with respect to the remaining ionic core electrons. Our method supports multiple electronic excitations within the neutral molecule. We calculated the channel-resolved ionization yields to each of the ionic electronic states. To compare with experiment, we additionally averaged these channel-resolved ionization rates over the random lab frame distribution of molecules axes. We calculated the ionization rates using a single half-cycle of the driving laser field, reflecting the subcycle ionization rates and excluding any multicycle response. The use of a half-cycle pulse is discussed and justified in the SOM. In Fig. 3A, we present the results of the calculated channel-resolved SFI yields for the dominant conformers (insets) of 1,3-butadiene (left) and n-butane (right) at a peak intensity of 1.5 × 1013 W/cm2. For 1,3-butadiene, ionization into the ionic ground state is the dominant channel, with some direct ionization into the first electronically excited state and higher lying channels. This result is in good agreement with the mass spectrum and CRATI results shown in Fig. 1. For the dominant anticonformer of n-butane (right), the calculations show that SFI into the first and higher lying electronically excited ionic states is favored over the ground-state channel. Once again, this agrees well with the experimental mass spectrum and CRATI results for n-butane (Fig. 2). These theoretical results show that direct ionization into multiple ionic states can be understood as a subcycle phenomenon. Qualitatively, the SFI response of these two molecules can be understood by considering the ionization energies and Dyson orbitals given in table S4. The Dyson orbitals represent the initial single-particle state of the ionizing electron. Within the Hartree-Fock approximation and Koopmans picture, they become ionization channels from the HOMO, HOMO–1, HOMO–2, etc. In a tunneling picture, SFI depends exponentially on the IP through the Keldysh factor exp[–(2/3)(2IP)3/2/E0]. Furthermore, for diatomics (37) it is known that nodal planes in the Dyson orbitals can cause strong suppression of the total yield of SFI. For the case of 1,3-butadiene, although the 12Au excited state has fewer nodal planes than the 12Bg ground state, the large energy gap favors the ground state. For the case of n-butane, where the energy gaps are much smaller, orbital symmetry effects become more pronounced. The Dyson orbitals for n-butane reveal that the 22Ag excited state has the fewest nodal planes; hence, this state experiences the least suppression, rendering it the dominant SFI channel as seen in Fig. 3A.

Fig. 3

(A) TDSE calculations of half-cycle ionization yields for producing the lowest few ionic states for the dominant conformers of 1,3-butadiene (left) and n-butane (right). The intensity was set to 1.5 × 1013 W/cm2 at a wavelength of 800 nm. For 1,3-butadiene, ground-state ionization is strongly favored, whereas for n-butane excited-state ionization is more probable. For more details, see the SOM. (B) TDSE calculations of half-cycle ionization yields for n-butane into the 2Ag ionic ground state and the strongest coupled ionic excited state (2Bu), shown both with (purple) and without (blue) laser-driven nonresonant interchannel dipole coupling (also known as NME) between the ionic states, for a higher intensity of 1.5 × 1014 W/cm2 at a wavelength of 800 nm. Channel-resolved ionization yields for two molecular frame field directions, x and y, are presented in the middle and right panels, respectively. The left panel shows the n-butane molecular frame relative to the x and y axes. NME considerably affects both ionization yields and electronic population redistribution among the ionic states within a half field cycle, and these effects are alignment-sensitive. For more details, see the SOM. au, atomic units.

An important question is the role of laser-driven nonadiabatic interchannel coupling (also known as NME) in polyatomics. As discussed in the SOM, the hydrocarbons irradiated here at a peak intensity of ~1013 W/cm2 (798 nm) exhibited predominantly adiabatic multichannel SFI dynamics. However, at higher intensities, the role of NME in even simple diatomics remains under active debate (6, 15). With our TDSE method, we can artificially turn off the laser-driven interchannel coupling in the theory and compare the result to the case where the coupling is retained. This procedure accentuates the effects of NME on the ionic-state population distribution during SFI. In Fig. 3B, we present theoretical channel-resolved SFI yields in n-butane using a half-cycle pulse of higher intensity (1.5 × 1014 W/cm2, 800 nm), both with (purple) and without (blue) NME coupling. For simplicity, only the 2Ag ground state and the 2Bu excited state were included, as these are the continuum channels most strongly dipole-coupled by the field. As seen in Fig. 3B, along two molecular frame directions x (middle) and y (right), coherent subcycle redistribution of population between electronic continuum channels occurs when NME is included. This qualitatively demonstrates that, at intensities typical of HHG experiments, the nonadiabatic population of multiple electronic continua can be another important contributor to the attosecond molecular response.

Although the present study does not address the tacit coherences created between ionic states (2), the CRATI method directly reveals the population of multiple electronic continua in the SFI of polyatomic molecules. A future extension of this method that measures fragment ion energy and/or angular distributions will be of interest. Studying CRATI spectra as a function of molecular electronic structure, molecular frame alignment, and laser frequency/intensity will illuminate the role of multiple electronic continua in attosecond SFI spectroscopies such as HHG.

Supporting Online Material


SOM Text

Figs. S1 to S6

Tables S1 to S4

References (4045)

References and Notes

  1. Acknowledgments: We thank the Natural Sciences and Engineering Research Council of Canada for financial support and R. Lausten, B. J. Sussman, D. J. Moffatt, and D. Guay for expert assistance. J.M. thanks the Feodor Lynen program of the Alexander von Humboldt Foundation for financial support. Aspects of this work are part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). The authors declare no competing financial interests.
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