Strong-field photoelectron momentum imaging of the prototypical biomolecule indole was disentangled in a combined experimental and computational approach. Experimentally, strong control over the molecules enabled the acquisition of photoelectron momentum distributions in the molecular frame for a well-defined, narrow range of incident intensities. A novel, highly efficient semiclassical simulation setup based on the adiabatic tunneling theory quantitatively reproduced these results. Jointly, experiment and computations revealed holographic structures in the asymptotic momentum distributions, which were found to sensitively depend on the alignment of the molecular frame. We identified the essential molecular properties that shape the photoelectron wavepacket in the first step of the ionization process and employ a quantum-chemically exact description of the cation during the subsequent continuum dynamics. The detailed modeling of the molecular ion, which accounts for its polarization by the laser-electric field, enables the simulation of laser-induced electron diffraction off large and complex molecules and provides full insight into the photoelectron's dynamics in terms of semiclassical trajectories. This provides the computational means to unravel strong-field diffractive imaging of biomolecular systems on femtosecond time scales.
We present a detailed comparison of strong-field ionization of diatomic molecules and their companion atoms with nearly equal ionization potentials. We perform calculations in the length and velocity gauge formulations of the molecular strong-field approximation and with the molecular tunneling theory, and in both cases we consider effects of nuclear motion. A comparison of our results with experimental data shows that the length gauge strong-field approximation gives the most reliable predictions.
The multiphoton ionization rate of molecules depends on the alignment of the molecular axis with respect to the ionizing laser polarization. By studying molecular frame photo-electron angular distributions from N$_2$, O$_2$ and benzene, we illustrate how the angle-dependent ionization rate affects the photo-electron cutoff energy. We find alignment can enhance the high energy cutoff of the photo-electron spectrum when probing along a nodal plane or when ionization is otherwise suppressed. This is supported by calculations using a tunneling model with a single ion state.
A model based on the strong-field and Born-Oppenheimer approximations qualitatively describes the distribution over vibrational states formed in a diatomic molecular ion following ionization of the neutral molecule by intense laser pulses. Good agreement is found with a recent experiment [X. Urbain et al., Phys. Rev. Lett. 92, 163004 (2004)]. In particular, the observed deviation from a Franck-Condon-like distribution is reproduced. Additionally, we demonstrate control of the vibrational distribution by a variation of the peak intensity or a change of frequency of the laser pulse.
We solve the hydrodynamic-ballistic equations of motion for a one-dimensional time-dependent Thomas-Fermi model of Cl_2 exposed to an intense subpicosecond laser field, and observe simultaneous multielectron ionization and molecular dissociation. The fragment kinetic energy defect with respect to the simple Coulomb explosion picture is found to originate in ejected-electron screening of the escaping fragments; its magnitude agrees with that observed in recent experiments.
Using a three-dimensional quasiclassical technique we explore the double ionization pathways of a diatomic molecule driven by an intense infrared (800nm) ultrashort laser pulse. For intensities corresponding to the tunneling regime, we find that the three main ionization mechanisms have distinct traces when considering the sum of the momenta parallel to the laser field as a function of the inter-electronic angle of escape. In addition, we find that the previously observed "finger-like" structure in the correlated momenta of the strongly driven He is also present for strongly driven diatomic mo…
We investigated electron emissions in strong field enhanced ionization of asymmetric diatomic molecules by quantum calculations. It is demonstrated that the widely-used intuitive physical pic- ture, i.e., electron wave packet direct ionization from the up-field site (DIU), is incomplete. Besides DIU, we find another two new ionization channels, the field-induced excitation with subsequent ionization from the down-field site (ESID), and the up-field site (ESIU). The contributions from these channels depend on the molecular asymmetry and internuclear distance. Our work provides a more comprehens…
The orientation-dependent strong-field ionization of CO molecules is investigated using the fully propagated three-dimensional time-dependent Hartree-Fock theory. The full ionization results are in good agreement with recent experiments. The comparisons between the full method and single active orbital (SAO) method show that although the core electrons are generally more tightly bounded and contribute little to the total ionization yields, their dynamics cannot be ignored, which effectively modify the behaviors of electrons in the highest occupied molecular orbital. By incorporating it into th…
Double ionization of diatomic molecules by short linearly polarized laser pulses is analyzed. We consider the final stage of the ionization process, that is the decay of a highly excited two electron molecule, which is formed after re-scattering. The saddles of the effective adiabatic potential energy close to which simultaneous escape of electrons takes place are identified. Numerical simulations of the ionization of molecules show that the process can be dominated by either sequential or non-sequential events. In order to increase the ratio of non-sequential to sequential ionizations very sh…
We consider the final stage of double ionization of $\rm O_2$ molecules by short linearly polarized laser pulses. The saddles of the effective adiabatic potential energy close to which simultaneous escape of electrons from a molecule takes place are identified. The analysis of the saddles and numerical simulations of the ionization indicate that to observe clear signatures of simultaneous electron escape in double ionization of $\rm O_2$ molecules stronger and much shorter laser pulses than those used in the recent experiment [E. Eremina, {\it et al}, Phys. Rev. Lett. {\bf 92}, 173001 (2004)] …
The geometry-dependent ionization behavior of the ammonia molecule is investigated. Different theoretical approaches for obtaining the ionization yield are compared, all of them showing a strong dependence of the ionization yield on the inversion coordinate at long wavelengths ($\geq$ 800 nm). It is shown how this effect can be exploited to create and probe nuclear wave packets in neutral ammonia using Lochfraß. Furthermore, imaging of a wave packet tunneling through the barrier of a double-well potential in real time is discussed.
We show that dynamic exchange is a dominant effect in strong field ionization of molecules. In $CO_2$ it fixes the peak ionization yield at the experimentally observed angle of $45^\circ$ between polarization direction and the molecular axis. In $N_2$ it changes the alignment dependence of yields by up to a factor of 2. The effect appears on the Hartree-Fock level as well as in full {\it ab initio} solutions of the Schrödinger equation.
We derive an analytical formula for the ionization rate of neutral atoms and molecules in a strong monochromatic field. Our model is based on the strong-field approximation with transition amplitudes calculated by an extended saddle point method. We show that the present two-term saddle point method reproduces even complicated structures in angular resolved photo electron spectra.
Trapping cold, chemically important molecules with electromagnetic fields is a useful technique to study small molecules and their interactions. Traps provide long interaction times that are needed to precisely examine these low density molecular samples. However, the trapping fields lead to non-uniform molecular density distributions in these systems. Therefore, it is important to be able to experimentally characterize the spatial density distribution in the trap. Ionizing molecules in different locations in the trap using resonance enhanced multiphoton ionization (REMPI) and detecting the re…
Using the molecular strong-field approximation we consider the effects of molecular symmetry on the ionization of molecules by a strong, linearly polarized laser pulse. Electron angular distributions and total ionization yields are calculated as a function of the relative orientation between the molecule and the laser polarization. Our studies focus on ethylene (C$_2$H$_4$), benzene (C$_6$H$_6$), fluorobenzene (C$_6$H$_5$F), and ortho chlorofluorobenzene (1,2 C$_6$H$_4$ClF), the molecules representing four different point groups. The results are compared with experiments, when available, and w…
We investigate electron correlation effects in internuclear-distance-dependent enhanced ionization of $\mathrm{H}_2$, $\mathrm{LiH}$, and $\mathrm{HF}$ molecules by intense near-infrared laser pulses using a 3D description of the systems with the time-dependent generalized-active-space configuration-interaction method. This method systematically incorporates electron-electron correlation of the quantum many-electron system under consideration. Our correlated description of diatomic molecules shows that enhanced ionization occurs at certain critical internuclear separations and electron correla…
We numerically study models of $\mathrm{H}_2$ and $\mathrm{LiH}$ molecules, aligned collinearly with the linear polarization of the external field, to elucidate the possible role of correlation in the enhanced-ionization phenomena. Correlation is considered at different levels of approximation with the time-dependent generalized-active-space configuration-interaction method. The results of our studies show that enhanced ionization occurs in multielectron molecules, that correlation is important and they also demonstrate significant deviations between the results of the single-active-electron a…
We investigate the differential ionization probability of chiral molecules in the strong field regime as a function of the helicity of the incident light. To this end, we analyze the fourfold ionization of bromochlorofluoromethane (CHBrClF) with subsequent fragmentation into four charged fragments and different dissociation channels of the singly ionized methyloxirane. We observe a variation of the differential ionization probability in a range of several percent. Accordingly, we conclude that the helicity of light is a quantity that should be considered for the theoretical description of the …
We formulate a three-dimensional semi-classical model to treat three-electron escape dynamics in a strongly-driven linear triatomic molecule, HeH$_{2}^{+}$. Our model includes the Coulomb singularities. Hence, to avoid unphysical autoionization, we employ two criteria to switch off the Coulomb repulsive force between two bound electrons and switch it on when the motion of one electron is mostly determined by the laser field. We investigate triple and "frustrated" triple ionization. In the latter process two electrons escape while one electron remains bound in a Rydberg state. We find that two …
Molecular helium represents a benchmark system for testing $\textit{ab initio}$ calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the $a\,^3Σ_u^+$ state of He$_2$, corresponding to the energy interval between the $a\,^3Σ_u^+$ ($v''=0$, $N''=1$) state of He$_2$ and the $X^+\,^2Σ_u^+$ ($v^+=0$, $N^+=1$) state of He${_2}^+$, and of the lowest rotational interval of He${_2}^+$. These measurements rely on the excitation of metastable He$_2$ molecules to high Rydberg states using frequency-comb-calibrated continuous-wave UV radiation in a co…
We study ionization of aligned H$_2^+$ in strong elliptically-polarized laser fields numerically and analytically. The calculated offset angle in photoelectron momentum distribution is several degrees larger for the molecule than a model atom with similar ionization potential at diverse laser parameters. Using a strong-field model that considers the properties of multi-center and single-center Coulomb potentials, we are able to quantitatively reproduce this angle difference between the molecule and the atom. Further analyses based on this model show that the response time of electron to light …
Using a semi-classical model, we study the formation of highly excited neutral fragments during the fragmentation of $\mathrm{H_3^+}$, a two-electron triatomic molecule, driven by an intense near-IR laser field. To do so, we first formulate a microcanonical distribution for arbitrary one-electron triatomic molecules. We then study frustrated double and single ionization in strongly-driven $\mathrm{H_3^+}$ and compute the kinetic energy release of the nuclei for these two processes. Moreover, we investigate the dependence of frustrated ionization on the strength of the laser field as well as on…
We extend the semiclassical two-step model for strong-field ionization that describes quantum interference and accounts for the Coulomb potential beyond the semiclassical perturbation theory to the hydrogen molecule. In the simplest case of the molecule oriented along the polarization direction of a linearly polarized laser field, we predict significant deviations of the two-dimensional photoelectron momentum distributions and the energy spectra from the case of atomic hydrogen. Specifically, for the hydrogen molecule the electron energy spectrum falls off slower with increasing energy, and th…
Using a semi-classical model, we investigate frustrated double ionization (FDI) in $\mathrm{D_3^+}$, a two-electron triatomic molecule, when driven by an intense, linearly polarized, near-infrared (800 nm) laser field. We compute the kinetic energy release of the nuclei and find a good agreement between experiment and our model. We explore the two pathways of FDI and show that, with increasing field strength, over-the-barrier ionization overtakes tunnel ionization as the underlying mechanism of FDI. Moreover, we compute the angular distribution of the ion fragments for FDI and identify a featu…
In the strong field molecular tunneling ionization theory of Tong et al. [Phys. Rev. A 66, 033402 (2002)], the ionization rate depends on the asymptotic wavefunction of the molecular orbital from which the electron is removed. The orbital wavefunctions obtained from standard quantum chemistry packages in general are not good enough in the asymptotic region. Here we construct a one-electron model potential for several linear molecules using density functional theory (DFT). We show that the asymptotic wavefunction can be improved with an iteration method and after one iteration accurate asymptot…
We theoretically investigate the mechanism of enhanced ionization in two-electron molecules by analyzing Bohmian trajectories for a one-dimensional H2 in an intense laser field. We identify both types of ionizing trajectories corresponding to the ejection from the up-field and down-field cores. The trajectories of the two electrons are correlated with each other in the former while correlation is negligible in the latter. The contributions from the two ionization types, though depending on laser intensity and internuclear distance, are comparable to each other.
Fully differential cross sections are calculated for the ionization of H$_2$ by fast charged projectiles using a semiclassical model developed previously for the ionization of atoms. The method is tested in case of 4 keV electron and 6 MeV proton projectiles. The obtained results show good agreement with the available experimental data. Interference effects due to the two-center character of the target are also observed and analyzed.
It has been recently predicted theoretically that due to nuclear motion light and heavy hydrogen molecules exposed to strong electric field should exhibit substantially different tunneling ionization rates (O.I. Tolstikhin, H.J. Worner and T. Morishita, Phys. Rev. A 87, 041401(R) (2013) [1]). We studied that isotope effect experimentally by measuring relative ionization yields for each species in a mixed H2/D2 gas jet interacting with intense femtosecond laser pulses. In a reaction microscope apparatus we detected ionic fragments from all contributing channels (single ionization, dissociation,…
Molecules show a much increased multiple ionization rate in a strong laser field as compared to atoms of similar ionization energy. A widely accepted model attributes this to the action of the joint fields of the adjacent ionic core and the laser on its neighbor inside the same molecule. The underlying physical picture for the enhanced ionization is that the up-field atom that gets ionized. However, this is still debated and remains unproven. Here we report an experimental verification of this long-standing prediction. This is accomplished by probing the two-site double ionization of ArXe, whe…
Strong-field ionization with few-cycle, mid-infrared laser pulses induces a localized ionization followed by long-lasting charge migration in halogenated organic molecules
We coincidently measure the molecular frame photoelectron angular distribution and the ion sum-momentum distribution of single and double ionization of CO molecules by using circularly and elliptically polarized femtosecond laser pulses, respectively. The orientation dependent ionization rates for various kinetic energy releases allow us to individually identify the ionizations of multiple orbitals, ranging from the highest occupied to the next two lower-lying molecular orbitals for various channels observed in our experiments. Not only the emission of a single electron, but also the sequentia…
Visualizing intense laser field driven electron dynamics in a multielectron molecule: dynamic electron localization, bonding properties and multiple ionization bursts
Chiral molecules ionized by circularly polarized fields produce a photoelectron current orthogonal to the polarization plane. This current has opposite directions for opposite enantiomers and provides an extremely sensitive probe of molecular handedness. Recently, such photoelectron currents have been measured in the strong-field ionization regime, where they may serve as an ultrafast probe of molecular chirality. Here we provide a mechanism for the emergence of such strong-field photoelectron currents in terms of two propensity rules that link the properties of the initial electronic chiral s…
Diatomic molecules (e.g., O$_2$) in intense laser field exhibit a peculiar suppressed ionization behavior compared to their companion atoms. Several physical models have been proposed to account for this suppression while no consensus has been achieved. In this letter, we aim to clarify the underlying mechanisms behind this molecular ionization suppression. Experimental data recorded at midinfrared laser wavelength and its comparison with that at near-infrared wavelength revealed a peculiar wavelength and intensity dependence of the suppressed ionization of O$_2$ with respect to its companion …
Angular distribution of photoelectrons released by the ionization of randomly-oriented molecules with two laser fields of carrier frequencies $ω$ and $2ω$, which are linearly polarized in two mutually-orthogonal directions, is analyzed in the perturbation limit for the case of one- vs two-photon ionization process. In particular, we focus on the recently predicted [Ph.V. Demekhin {\it et al.}, Phys. Rev. Lett. \textbf{121}, 253201 (2018)] forward-backward asymmetry in the photoelectron emission, which is induced by the interference of two fields and depends on the external relative phase betwe…
The combination of photoelectron spectroscopy and ultrafast light sources is on track to set new standards for detailed interrogation of dynamics and reactivity of molecules. A crucial prerequisite for further progress is the ability to not only detect the electron kinetic energy, as done in traditional photoelectron spectroscopy, but also the photoelectron angular distributions (PADs) in the molecular frame. Here carbonylsulfide (OCS) and benzonitrile molecules, fixed in space by combined laser and electrostatic fields, are ionized with intense, circularly polarized, 30 femtosecond laser puls…
Study on ionization process of molecules in an intense infrared laser field is of paramount interest in strong-field physics and constitutes the foundation of imaging of molecular valence orbitals and attosecond science. We show measurement of alignment-dependent ionization probabilities of the lower-lying orbitals of the molecules by experimentally detecting alignment-dependence of fluorescence emission from tunnel ionized carbon dioxide molecules. The experimental measurements are compared with the theoretical calculations of strong field approximation (SFA) and molecular ADK models. Our res…
In few-cycle pulses, the exact value of the carrier-envelope phase difference (CEPD) has a pronounced influence on the ionization dynamics of atoms and molecules. We show that for atoms in circularly polarized light, a change in the CEPD is mapped uniquely to an overall rotation of the system, and results for arbitrary CEPD are obtained by rotation of the results from a single calculation with fixed CEPD. For molecules this is true only for linear molecules aligned parallel with the propagation direction of the field. The effects of CEPD are classified as geometric or non-geometric. The observ…
We revisit strong-field ionization of aligned O$_2$, CO$_2$, and CS$_2$ molecules in light of recent advances in the field of strong-field physics, in particular the inclusion of multielectron polarization in the numerical solution of the time-dependent Schr{ö}dinger equation (TDSE) within the singe-active-electron approximation. Upon inclusion of multielectron polarization and the associated induced dipole potential in the TDSE model, we obtain angular distributions of total ionization yields which are in better agreement with the available experimental results for CO$_2$ and CS$_2$. For the …
The direct above-threshold ionization (ATI) of diatomic molecules in linearly-polarized infrared and extreme ultraviolet (IR+XUV) laser fields is investigated by the frequency-domain theory based on the nonperturbative quantum electrodynamics. The destructive interference fringes on the angle-resolved ATI spectra, which are closely related to the molecular structure, can be well fitted by a simple predictive formula for any alignment of the molecular axis. By comparing the direct ATI spectra for monochromatic and two-color laser fields, we found that the XUV laser field can both raise the ioni…
In this communication, we present the results of the triple differential cross-section (TDCS) for the (e,2e) process on H2O molecule for the plane wave and the twisted electron beam impact. The formalism is developed in the first Born approximation. We describe the plane/twisted wave, plane wave, the linear combination of atomic orbitals (LCAO) (self-consistent field LCAO method) and Coulomb wave for the incident electron, scattered electron, the molecular state of H2O, and the ejected electron, respectively. We investigate the angular profiles of the TDCS for the outer orbitals 1B1, 3A1, 1B2,…
Ionization and excitation of water molecules in intense laser pulses is studied theoretically by solving the three-dimensional time-dependent electronic Schrödinger equation within the single-active-electron approximation. The possibility to image orbital densities by measurement of the orientation-dependent ionization of H2O in few-cycle, 800nm linear-polarized laser pulses is investigated. While the highest-occupied molecular orbital 1b1 is found to dominate the overall ionization behavior, contributions from the energetically lower lying 3a1 orbital dominate the ionization yield in the noda…
We formulate a computationally efficient time-independent method based on the multi-electron molecular R-matrix formalism. This method is used to calculate transition matrix elements for the multi-photon ionization of atoms and molecules under the influence of a perturbative field. The method relies on the partitioning of space which allows us to calculate the infinite-range free-free dipole integrals analytically in the outer region, beyond the range of the initial bound wave function. This approach is valid for an arbitrary order, that is, any number of photons absorbed both in the bound and…
We report an upper bound to the ionization energy of 85Rb2 of 31348.0(6) cm-1, which also provides a lower bound to the dissociation energy D0 of 85Rb2+ of 6307.5(6) cm-1. These bounds were measured by the onset of autoionization of excited states of 85Rb2 below the 5s+7p atomic limit. We form 85Rb2 molecules via photoassociation of ultracold 85Rb atoms, and subsequently excite the molecules by single-photon ultraviolet transitions to states above the ionization threshold.
We discuss the mechanism by which the inclusion of multielectron polarization improves the solution of the time-dependent Schrödinger equation (TDSE) for the oriented CO molecule in a strong external laser pulse within the single-active-electron (SAE) approximation. A challenging problem of using the SAE approximation is that the active electron, instead of undergoing ionization, may be driven by the external field to lower-lying orbitals. For the oriented CO molecule, dipole coupling to the lower-lying bound states of the potential depends on the orientation angle, thereby affecting the orien…
We address the influence of the orbital symmetry and of the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules, in the length and velocity gauges. We work within the strong-field approximation and assume that the second electron is dislodged by electron-impact ionization, and also consider the classical limit of this model. We show that the electron-momentum distributions exhibit interference maxima and minima due to the electron emission at spatially separated centers. The interference patterns survive the in…
We study frustrated double ionization in a strongly-driven heteronuclear molecule HeH$^{+}$ and compare with H$_2$. We compute the probability distribution of the sum of the final kinetic energies of the nuclei for strongly-driven HeH$^{+}$. We find that this distribution has more than one peak for strongly-driven HeH$^{+}$, a feature we do not find to be present for strongly-driven H$_{2}$. Moreover, we compute the probability distribution of the n quantum number of frustrated double ionization. We find that this distribution has several peaks for strongly-driven HeH$^{+}$, while the respecti…
A general model and toolkit for the ionization of three or more electrons in strongly driven molecules using an effective Coulomb potential for the interaction between bound electrons
Using a three-dimensional quasiclassical technique we explore molecular double ionization by a linearly polarized, infrared (800~nm) 27~fs laser pulse. For intensities ranging from the tunneling to the over-the-barrier regime, we identify the double ionization pathways in a unified way as a function of total electron energy. For the tunneling regime, we discuss the differences in the interplay of double ionization (DI) pathways between strongly driven He and strongly driven $N_{2}$. For intermediate intensities in the over-the-barrier regime, we find that both the correlated momenta and the do…
Accurate molecular imaging via high-order harmonic generation relies on comparing the harmonic emission from a molecule and an adequate reference system. However, an ideal reference atom with the same ionization properties as the molecule does not always exist. We show that for suitably designed, very short laser pulses, a one-to-one mapping between high-order harmonic frequencies and electron momenta in above-threshold ionization exists. Comparing molecular and atomic momentum distributions then provides the electron return amplitude in the molecule for every harmonic frequency. We show that …
We report on the fragmentation of the water molecule by $1$ MeV H$^{+}$, He$^{+}$ and 650 keV N$^{+}$ ion impact. The fragment-ion energy spectra were measured by an electrostatic spectrometer at different observation angles. The obtained double-differential fragmentation cross sections for N$^{+}$ is found to be more than an order of magnitude higher, than that for H$^{+}$. The relative ratios of the fragmentation channels are also different for the three projectiles. Additional fragmentation channels were observed in the spectra for He$^{+}$ and for N$^{+}$ impact, which are missing in the c…
We demonstrate sub-cycle control of frustrated double ionization (FDI) in the two-electron triatomic molecule D$_3^+$ when driven by two orthogonally polarized two-color laser fields. We employ a three-dimensional semi-classical model that fully accounts for the electron and nuclear motion in strong fields. We control FDI triggered by a strong near-infrared laser field with a weak mid-infrared laser field. This control as a function of the time delay between the two pulses is demonstrated when the FDI probability and the distribution of the momentum of the escaping electron along the mid-infra…
A new simulation box setup is introduced for the precise description of the wavepacket evolution of two electronic systems in intense laser pulses. In this box, the regions of the hydrogen molecule H$_{2} $, and singly and doubly ionized species, H$_{2}^+ $ and H$_{2}^{+2} $, are well recognized and their time-dependent populations are calculated at different laser field intensities. In addition, some new regions are introduced and characterized as quasi-double ionization and their time-dependencies on the laser field intensity are calculated and analyzed. The adopted simulation box setup is s…
We demonstrate the control of electron-electron correlation in frustrated double ionization (FDI) of the two-electron triatomic molecule D$_{3}^{+}$ when driven by two orthogonally polarized two-color laser fields. We employ a three-dimensional semi-classical model that fully accounts for the electron and nuclear motion in strong fields. We analyze the FDI probability and the distribution of the momentum of the escaping electron along the polarization direction of the longer wavelength and more intense laser field. These observables when considered in conjunction bear clear signatures of the p…
