Pathway-resolved photoelectron emission in dissociative ionization of molecules

X. GONG, P. HE, Q. SONG, Q. JI, K. LIN, W. ZHANG, P. LU, H. PAN, J. DING, H. ZENG, F. HE, AND J. WU State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China Key Laboratory of Laser Plasmas (Ministry of Education) and Department of Physics and Astronomy, Collaborative Innovation Center for IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Anhui 230026, China Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China e-mail: hpzeng@phy.ecnu.edu.cn e-mail: fhe@sjtu.edu.cn e-mail: jwu@phy.ecnu.edu.cn

Electron-ion coincidence detection allows one to visualize the ultrafast chemical reactions of molecules in strong laser fields.Here, by measuring the photoelectron angular distribution (PAD) of H 2 in strong laser fields correlated to different pathways, i.e., direct ionization when the internuclear distance is small, or ionization after the molecular bond stretches to a large internuclear distance, we uncover the roles of the molecular orientation and internuclear distance in the dissociative ionization of H 2 .As compared to the first dissociation pathway, the regular nodal structures on the concentric above-threshold ionization circles vanish for the second pathway, which are numerically validated by the quantum simulations.Pathway-resolved PADs assisted by electron-ion coincidence detection open new possibilities to probe the rich dynamics of molecules in strong laser fields, in particular to image the instantaneous geometry of molecules.Single-and multiphoton-ionization of atoms and molecules in external fields have been well studied to probe the electronic and nuclear dynamics [1][2][3].The photoelectron angular distribution (PAD) [4] of the above threshold ionization (ATI) in the multiphoton ionization regime manifests itself as multiple concentric circles shaped with regular nodal structures [5][6][7][8].In tunneling ionization, the released electron wave packet flows mainly along the laser polarization axis without the regular nodal structure [9].The tunneled electron mostly ends at zero momentum along the field direction of the linearly polarized pulse [10], or is angularly streaked by an elliptically polarized pulse [11].
As compared to atoms, the PADs of molecules depend not only on the binding energies but also on the molecular orientation and geometry [12][13][14] at the instant of electron release.It imprints the instantaneous electronic and nuclear structures of the molecule [15,16], which makes it very attractive for real-time imaging of the structure of an isolated molecule [17] and to probe the rich dynamics of photoionization [4,18,19].A molecule in strong laser fields may undergo different chemical reaction pathways.One problem would be how the molecular orientation and internuclear distance play roles for these different pathways.Conversely and more challengingly, is it possible to experimentally disentangle the coexisting different dynamics for various reaction pathways?Pathway-resolved PADs assisted by electron-ion coincidence detection open the possibility to uncover the concurrent molecular-orientation and internuclear-distance dependences.
In this Letter, by resolving the multiphoton ATI of H 2 into various dissociation pathways, we observe distinct PADs driven by an intense femtosecond laser pulse.We identified two dissociative ionization pathways, as shown in Fig. 1(a).First, H 2 is singly ionized around its equilibrium distance, and the resultant H 2 undergoes bond-softening dissociation [20,21] by absorbing one extra photon.Second, the neutral H 2 may be excited to an intermediate state by absorbing multiple photons and stretch to a large internuclear distance.The stretched H 2 may absorb few extra photons, giving birth to a free electron, meanwhile launching the nuclear wave packet on the dissociative state, which ultimately gains a little kinetic energy.We name these two dissociation pathways, respectively, post-ionization dissociation [22][23][24] and stretched-bond ionization pathways.Here we observe distinct PADs correlated to the post-ionization dissociation and stretched-bond ionization pathways.This is inherent and unique for molecules as compared to atoms, which cannot be revealed by tracing the PAD correlated to the non-dissociative H 2 [25].
Our experimental measurements are performed in an ultrahigh vacuum chamber of cold target recoil ion momentum spectroscopy (COLTRIMS) [26,27].Femtosecond laser pulses with various wavelengths and temporal durations are focused onto a supersonic gas jet of H 2 by a concave silver mirror (f 7.5 cm) inside the vacuum chamber.The three-dimensional momentum vectors of the measured protons and electrons are reconstructed from the times of flight and positions detected by two time-and position-sensitive microchannel plate detectors at opposite ends of the spectrometer (Supplement 1).In the following, we will first use a 60 fs, 395 nm ultraviolet (UV) pulse to demonstrate the pathway-resolved PADs of the H 2 mℏω → H H e channel with m being an integer, labeled H 2 1; 0, and then its dependences on the field intensity and central wavelength of the laser pulses.Here, we use the concept of pathway to label the dissociation process as widely used in the dissociative ionization of H 2 by laser fields of modest intensities [23,24].As compared to previous works using weak fields of high photon energies [28,29], a yield ratio of 3∶1 between the dissociative and non-dissociative single ionization pathways is observed in our experiments.
The two dissociation pathways give distinct nuclear kinetic energy release E N .For the post-ionization dissociation, the E N peaks around 1.5 eV, which is consistent with previous measurements [22][23][24].On the other hand, stretched-bond ionization happens when the internuclear distance is already very large, resulting in a low E N , as shown in the inset (top) in Fig. 1(a).
Besides the E N , the emitted electrons associated with these two pathways present distinct PADs.The post-ionization electron spectra are collected in coincidence with the H fragment energy of 1.5 0.5 eV.The stretched-bond electron spectra are collected in coincidence with the H fragment energy of 0.25 0.25 eV.Using this coincidence, we separate these two different pathways and show the corresponding photoelectron spectra in Figs.1(b) and 1(c).The regular nodal structures observed on the concentric ATI circles of the post-ionization dissociation pathway [Fig.1(b)] disappear for the stretched-bond ionization pathway [Fig.1(c)].The electron kinetic-energy-integrated PADs of three low ATI orders are correspondingly displayed in the top insets of Figs.1(b) and 1(c).As compared to previous work on the electron detachment processes of a molecular anion [14], here we directly resolve the PADs into various dissociative ionization pathways of a neutral molecule.As shown in Fig. 2, distinct PADs of two dissociative ionization pathways are observed for a wide range of field intensity of the UV pulse from 0.5 to 1.5 × 10 14 W∕cm 2 .To show that the pathway-resolved distinct PADs are not unique for the 395 nm UV pulse, we adjusted the central wavelength of the laser pulse using traveling-wave optical parametric amplifier superfluorescence.Similar to the 395 nm UV pulse, the post-ionization dissociation and stretched-bond ionization pathways are featured with distinct PADs when the wavelength is shorter than 550 nm.For instance, Figs.2(g) and 2(h) display the pathway-resolved distinct PADs for a 510 nm femtosecond laser pulse.
Concentric ATI circles with regular nodal structures are typically observed for the multiphoton single ionization of atoms and molecules [5,7,[30][31][32].The regular nodal structure is understood as the intracycle interference of the released electronic wave packets [7,8,18,19], which also encodes the quantum number of the angular momentum of the freed electron [25,33,34].As shown in Figs.2(a), 2(c), and 2(e), the additional nodes on the near-threshold ionization ATI circle (S 0) appear only at high field intensities and shift to lower energies due to the long-range Coulomb potential [33][34][35][36].As displayed in the inset of Fig. 1(a), similar concentric ATI circles with regular nodal structures are observed for the non-dissociative H 2 , which is mostly generated by ionizing H 2 around the equilibrium internuclear distance R 1.4 a.u.Correspondingly, as shown in Fig. 3(a), the positions of the nodes and local maxima in the  PAD of the post-ionization dissociation pathway are independent of the orientation of H 2 .
The role of the molecular orientation in photoionization processes becomes significant when the electron is released at a large internuclear distance.As shown in Fig. 3(b), the PAD of the stretched-bond ionization pathway clearly depends on the orientation of H 2 , especially for electrons emitting away from the field polarization direction, whose local maximal positions gradually change as marked by the white dashed curves.As shown in Fig. 3(c), the angular nodal structures sensitively depend on the molecular orientation.These fine structures are averaged out by integrating over the absolute value of the molecular orientation angle θ H from 0°to 180°, resulting in a tunneling-like PAD featured with dominant distribution along the polarization direction of the laser field.As illustrated in Fig. 1(a), one possible process for the stretched-bond ionization pathway is: first, H 2 absorbs four photons and is excited to an intermediate state, e.g., the double-well EF 1 Σ g state about 13 eV above the ground state of H 2 [25,28,29,37,38]; second, the excited H 2 may stretch to a large internuclear distance around R ∼ 6 a.u.; third, the stretched H 2 is singly ionized by absorbing two extra photons while the nuclear wave packet is tossed onto the dissociative potential surface and finally dissociates into H H with little E N .The EF 1 Σ g state is the most likely intermediate for the stretchedbond ionization pathway in our UV pulse because it lies in the proper energy range of four photons with the right parity for the dipole-allowed transition from the ground state X 1 Σ g of H 2 .Meanwhile, its double-well structure with the F-well around R 6 a.u.increases the probability of observing the stretched-bond ionization pathway by freeing an electron at a large internuclear distance.As shown in the inset of Fig. 1(a), the stretched-bond ionization pathway is favored for laser pulses of long temporal durations in which the molecule has enough time to elongate to a large internuclear distance where the electron is freed.Here, a 22-fs UV pulse was generated by frequency doubling a precompressed few-cycle pulse from the output of a Ne-filled hollow fiber.The UV pulse was alternatively temporally stretched to 112 fs by inserting several pieces of fused silica glasses (Supplement 1).
We numerically simulated the time-dependent Schrödinger equation (TDSE) with the single active electron approximation to test the PADs (Supplement 1).We calculated the singleionization-induced PADs at R 1.4 and 6 a.u., standing for the electron release at small and large internuclear distances, respectively.The simulated PADs for R 6 a.u.are shown in Figs.4(a)-4(c), respectively corresponding to the absolute value of the cross angles jθ H j 0°, 30°, and 60°.Hence, for example, Fig. 4(b) is the averaged results for θ H 30°and −30°, which preserves the left-right symmetry for the PAD.The fine structures of the simulated PADs vary as the molecule orients at different angles.As a result, the orientation-averaged overall PAD [Fig.4(d)] is maximized along the polarization direction of the laser field.However, for R 1.4 a.u., as shown in Figs.4(e)-4(g), the simulated PADs are nearly independent of the molecular orientation.The regular nodal structures on the ATI circles thus survive in the overall PAD after the orientation average.Figures 4(d) and 4(h) capture the main features of the experiments and thus confirm the roles of molecular orientation at various internuclear distances for two different dissociative ionization pathways.One may note that our modeled TDSE cannot precisely describe the electronic state of EF 1 Σ g at R 6 a.u.; however, our test simulations show that the PADs are not sensitive to the details of the initial electronic state of the bondstretched molecule, but are dominated by the orientation of the molecular axis with respect to the laser polarization.
To understand the orientation-dependent PADs for electron release at various internuclear distances, Fig. 3(d) shows the calculated saddle position y s ; z s in the plane composing the molecular axis and the laser electric field by setting ∂V R; x; y; z∕ ∂y 0, ∂V R; x; y; z zE∕∂z 0 and scanning the molecular orientation angle from 0 to 2π.The instantaneous electric field was E −0.053 a.u. and pointed to −z.The corresponding Keldysh parameters are 1.4 and 2.3 for the modeled molecule with internuclear distances of R 1.4 and 6 a.u., respectively, in which range the tunneling picture of the electron release still works well, as demonstrated in Refs.[39,40].When the internuclear distance is R 1.4 a.u., y s ; z s nearly does not change when the molecular orientation changes.However,  y s ; z s scatters in a relative large area when the internuclear distance is R 6 a.u.This will introduce different initial phases and subsequent Coulomb actions of the nuclei on the outgoing electrons.Hence, for different molecular orientations, the structure of the PADs, for example, the nodal structure ruled by the interference of the released electrons, are clearly different, which qualitatively explains the experimental observations and theoretical calculations.
In summary, by resolving the multiphoton single ionization of H 2 into various channels, we have observed distinct PADs for the post-ionization dissociation and stretched-bond ionization pathways.As compared to the post-ionization dissociation pathway, the regular nodes on the concentric ATI circles vanish for the stretched-bond ionization pathway.This is attributed to the molecular-orientation-and internuclear-distance-dependent photoelectron emission.By measuring the ejected electrons and ions in coincidence, the pathway-resolved PADs provide a powerful tool for revealing the complex dynamics of molecules in strong laser fields.

Fig. 1 .
Fig. 1.(a) Schematic diagram of the post-ionization dissociation and stretched-bond ionization pathways in multiphoton ionization of H 2 .The insets show the normalized kinetic energy release distribution of the H H (top, driven by laser pulses of different temporal durations), and the PAD correlated to H 2 (bottom) measured for the 60 fs, 395 nm UV pulse at I 0 1.1 × 10 14 W∕cm 2 .(b), (c) Measured PADs correlated to (b) the post-ionization dissociation and (c) the stretched-bond ionization pathways of the H 2 1; 0 channel.The top panels of (b) and (c) are the electron kinetic energy-integrated PADs of three ATI orders, where ϕ e is defined with respect to the laser polarization vector along the z axis.

Fig. 2 .
Fig. 2. Measured PADs correlated to the post-ionization dissociation (top row) and stretched-bond ionization (bottom row) pathways of the H 2 1; 0 channel at various laser intensities and wavelengths.The laser intensities of the 60 fs, 395 nm UV pulse are set to be (a), (b) 0.5; (c), (d) 0.7; and (e), (f) 1.5 × 10 14 W∕cm 2 .The central wavelength of the laser pulse is 510 nm in (g) and (h), and its intensity and temporal duration are 0.8 × 10 14 W∕cm 2 and 30 fs.

Fig. 3 .
Fig. 3. (a), (b) PADs of the second-order ATI (S 1) as a function of the molecular orientation correlated to the (a) post-ionization dissociation and (b) stretched-bond ionization pathways.To increase the visibility, the inset of (b) (top right) zooms in the molecular-orientationdependent PADs with a different color bar from 0 to 60 counts where the positions of the local maxima are marked by the white dashed lines.(c) The normalized and vertically offset slices of the PAD at θ H 7°, 50°, and 90°extracted from (b), which are fitted by using Legendre polynomials of P 5 n0 C 2n P 2n cosϕ e with proper coefficients C 2n .(d) Calculated saddle positions in the y-z plane for internuclear distance R 1.4 and 6.0 a.u.