Two-source double-slit interference in angle-resolved high-energy above-threshold ionization spectra of diatoms

Elliptic Dichroism in the Above-Threshold Ionization of Molecules Induced by a Strong Laser Field

Using a strong-field-approximation theory, we investigate the high-order above-threshold ionization of diatomic molecules exposed to the monochromatic and bichromatic elliptically polarized fields. We devote particular attention to the difference between the photoelectron momentum distributions obtained with fields with opposite helicity. This difference is quantified using the elliptic-dichroism parameter, which represents the normalized difference between the differential ionization rates calculated with driving fields with opposite helicity. We find that this parameter strongly depends on the molecular orientation with respect to the laser field. In addition, this dependence is different for molecules with different types of highest-occupied molecular orbital. In other words, we show that the molecular structure is imprinted onto the elliptic-dichroism parameter for both monochromatic and bichromatic driving fields. This is explained by analyzing the interferences between various partial contributions to the differential ionization rate. In this way, elliptic dichroism also serves as a tool to analyze the electron dynamics. Finally, for heteronuclear diatomic molecules, we show that the elliptic dichroism is different from zero even for the direct electrons, i.e., the electrons that after liberation go directly to the detector. In this case, the dependence on the molecular orientation is far more pronounced for a bichromatic driving field.

Elliptic dichroism in strong-field ionization of atoms subjected to tailored laser fields

The differential ionization rate for strong-field ionization by tailored laser fields of atomic systems averaged over the magnetic quantum number satisfies particular inversion and reflection symmetries. The symmetries of the elliptic-dichroism parameter, which is related to the change of sign of the ellipticity of the laser field, are considered in detail, with particular emphasis on high-order above-threshold ionization. The general results are illustrated by the examples of an elliptically polarized laser field and a bi-elliptical orthogonally polarized two-color (BEOTC) field. For the BEOTC field the differential ionization rate and the elliptic-dichroism parameter are investigated for the ω-2ω and ω-3ω field combinations and for various relative phases between the laser-field components. The inversion and reflection symmetries of the photoelectron momentum distribution in the polarization plane of the field depend on the parities of r and s in the rω--sω BEOTC field combination and on the relative phase between the field components. We suggest that, by analyzing the symmetry properties of the measured momentum distribution of the elliptic-dichroism parameter, one can identify the mechanism of strong-field ionization. If the rescattering mechanism is dominant one can use these distributions to obtain information about the atomic and molecular structure and dynamics.

Symmetries and Selection Rules of the Spectra of Photoelectrons and High-Order Harmonics Generated by Field-Driven Atoms and Molecules

Using the strong-field approximation we systematically investigate the selection rules for high-order harmonic generation and the symmetry properties of the angle-resolved photoelectron spectra for various atomic and molecular targets exposed to one-component and two-component laser fields. These include bicircular fields and orthogonally polarized two-color fields. The selection rules are derived directly from the dynamical symmetries of the driving field. Alternatively, we demonstrate that they can be obtained using the conservation of the projection of the total angular momentum on the quantization axis. We discuss how the harmonic spectra of atomic targets depend on the type of the ground state or, for molecular targets, on the pertinent molecular orbital. In addition, we briefly discuss some properties of the high-order harmonic spectra generated by a few-cycle laser field. The symmetry properties of the angle-resolved photoelectron momentum distribution are also determined by the dynamical symmetry of the driving field. We consider the first two terms in a Born series expansion of the T matrix, which describe the direct and the rescattered electrons. Dynamical symmetries involving time translation generate rotational symmetries obeyed by both terms. However, those that involve time reversal generate reflection symmetries that are only observed by the direct electrons. Finally, we explain how the symmetry properties, imposed by the dynamical symmetry of the driving field, are altered for molecular targets.

Ellipticity of High-Order Harmonics Generated by Aligned Homonuclear Diatomic Molecules Exposed to an Orthogonal Two-Color Laser Field

We investigate emission rate and ellipticity of high-order harmonics generated exposing a homonuclear diatomic molecule, aligned in the laser-field polarization plane, to a strong orthogonally polarized two-color (OTC) laser field. The linearly polarized OTC-field components have frequencies rω and sω, where r and s are integers. Using the molecular strong-field approximation with dressed initial state and undressed final state, we calculate the harmonic emission rate and harmonic ellipticity for frequency ratios 1:2 and 1:3. The obtained quantities depend strongly on the relative phase between the laser-field components. We show that with the OTC field it is possible to generate elliptically polarized high-energy harmonics with high emission rate. To estimate the relative phase for which the emission rate is maximal we use the simple man’s model. In the harmonic spectra as a function of the molecular orientation there are two types of minima, one connected with the symmetry of the molecular orbital and the other one due to destructive interference between different contributions to the recombination matrix element, where we take into account that the electron can be ionized and recombine at the same or different atomic centers. We derive a condition for the interference minima. These minima are blurred in the OTC field except in the cases where the highest occupied molecular orbital is modeled using only s or only p orbitals in the linear combination of the atomic orbitals. This allows us to use the interference minima to assess which atomic orbitals are dominant in a particular molecular orbital. Finally, we show that the harmonic ellipticity, presented in false colors in the molecular-orientation angle vs. harmonic-order plane, can be large in particular regions of this plane. These regions are bounded by the curves determined by the condition that the harmonic ellipticity is approximately zero, which is determined by the minima of the T-matrix contributions parallel and perpendicular to the fundamental component of the OTC field.

Tomographic Extraction of the Internuclear Separation Based on Two-Center Interference with Aligned Diatomic Molecules

We experimentally investigate the two-dimensional photoelectron momentum spectra of aligned diatomic molecules in an intense laser field. Our results reveal a novel prominent valley structure in the molecular alignment dependence of the high-energy photoelectron spectra along the laser polarization. Resorting to the molecular strong-field approximation and a simple semiclassical analysis, we show that this valley structure stems from the destructive two-center interference of the laser-driven rescattered electrons in diatomic molecules. Based on this two-center interference with aligned diatomic molecules, we demonstrate for the first time a tomographic method to extract the molecular internuclear separation, providing a more straightforward approach of molecular imaging, in comparison with, e.g., laser-induced electron diffraction and fixed-angle broadband laser-driven electron scattering.

Atomic and Molecular Processes in a Strong Bicircular Laser Field

With the development of intense femtosecond laser sources it has become possible to study atomic and molecular processes on their own subfemtosecond time scale. Table-top setups are available that generate intense coherent radiation in the extreme ultraviolet and soft-X-ray regime which have various applications in strong-field physics and attoscience. More recently, the emphasis is moving from the generation of linearly polarized pulses using a linearly polarized driving field to the generation of more complicated elliptically polarized polychromatic ultrashort pulses. The transverse electromagnetic field oscillates in a plane perpendicular to its propagation direction. Therefore, the two dimensions of field polarization plane are available for manipulation and tailoring of these ultrashort pulses. We present a field that allows such a tailoring, the so-called bicircular field. This field is the superposition of two circularly polarized fields with different frequencies that rotate in the same plane in opposite directions. We present results for two processes in a bicircular field: High-order harmonic generation and above-threshold ionization. For a wide range of laser field intensities, we compare high-order harmonic spectra generated by bicircular fields with the spectra generated by a linearly polarized laser field. We also investigate a possibility of introducing spin into attoscience with spin-polarized electrons produced in high-order above-threshold ionization by a bicircular field.

Dissociative Ionization of Argon Dimer by Intense Femtosecond Laser Pulses

We experimentally and theoretically studied dissociative ionization of argon dimer driven by intense femtosecond laser pulses. In the experiment, we measured the ion yield and the angular distribution of fragmental ions generated from the dissociative ionization channels of (1,1) (Ar₂²⁺ → Ar⁺ + Ar⁺) and (2,1) (Ar₂³⁺ → Ar²⁺ + Ar⁺) using a cold target recoil ion momentum spectroscopy. The channel ratio of (2,1)/(1,1) is 4.5-7.5 times of the yield ratio of double ionization to single ionization of argon monomer depending on the laser intensity. The measurement verified that the ionization of Ar⁺ is greatly enhanced if there exists a neighboring Ar⁺ separated by a critical distance. In addition, the fragmental ions exhibit an anisotropic angular distribution with the peak along the laser polarization direction and the full width at half maximum becomes broader with increasing laser intensity. Using a full three-dimensional classical ensemble model, we calculated the angle-dependent multiple ionization probability of argon dimer in intense laser fields. The results show that the experimentally observed anisotropic angular distribution of fragmental ions can be attributed to the angle-dependent enhanced ionization of the argon dimer in intense laser fields.

Intra-half-cycle interference of low-energy photoelectron in strong midinfrared laser fields

Using semiclassical models with implementing interference effects, we study the low-energy photoelectron intra-half-cycle interferences among nonscattering trajectories and multiple forward scattering trajectories of atoms ionized by a strong mid-infrared laser field. Tracing back to the initial tunneling coordinates, we find that up to three kinds of forward scattering trajectories have substantial contributions to the low-energy photoelectrons. Those multiple forward scattering trajectories depend sensitively on the initial transverse momentum at the tunnel exit and they lead to sign reversal of the transverse momentum of the electrons. We show that the interference of the nonscattering trajectory and the triple-scattered trajectory has the largest contribution to the low-energy structure in mid-infrared laser fields. It is also shown that the long-range Coulomb potential has a significant effect on the low-energy photoelectron interference patterns.

Phase Structure of Strong-Field Tunneling Wave Packets from Molecules

We study the phase structure of the tunneling wave packets from strong-field ionization of molecules and present a molecular quantum-trajectory Monte Carlo model to describe the laser-driven dynamics of photoelectron momentum distributions of molecules. Using our model, we reproduce and explain the alignment-dependent molecular frame photoelectron spectra of strong-field tunneling ionization of N_{2} reported by M. Meckel et al. [Nat. Phys. 10, 594 (2014)]. In addition to modeling the low-energy photoelectron angular distributions quantitatively, we extract the phase structure of strong-field molecular tunneling wave packets, shedding light on its physical origin. The initial phase of the tunneling wave packets at the tunnel exit depends on both the initial transverse momentum distribution and the molecular internuclear distance. We further show that the ionizing molecular orbital has a critical effect on the initial phase of the tunneling wave packets. The phase structure of the photoelectron wave packet is a key ingredient for modeling strong-field molecular photoelectron holography, high-harmonic generation, and molecular orbital imaging.

Photoelectron diffraction in methane probed via vibrationally resolved inner-valence photoionization cross-section ratios

Vibrationally resolved photoionization of the 2a1 orbital in methane has been studied both experimentally and theoretically, over a wide range of photon energies (40-475 eV). A vibrational progression associated with the symmetric stretch mode of the 2a1(-1) single-hole state was observed in the experimental photoelectron spectra. Individual vibrational sub-states of the spectra were found to be best modeled by asymmetric line-shapes with linewidths gradually increasing with the vibrational quantum number. This indicates the occurrence of a pre-dissociation process for the involved ionic state, discussed here in detail. Finally, diffraction patterns were observed in the vibrational branching ratios for the first three vibrational sub-states ("v-ratios") of the experimental photoelectron spectra. They are found to be in excellent qualitative agreement with those obtained from ab initio models. Compared with previous studies of the 1a1(-1) core-shell photoionization of methane, the period of oscillation of the v-ratios is found to be very different and the phases are of opposite signs. This suggests a strong interplay between the electron diffraction and interference effects inside the molecular potential.

Laser induced alignment of state-selected CH3I

Hexapole state selection is used to prepare CH3I molecules in the |JKM〉 = |1±1∓1〉 state. The molecules are aligned in a strong 800 nm laser field, which is linearly polarised perpendicular to the weak static extraction field E of the time of flight setup. The molecules are subsequently ionised by a second time delayed probe laser pulse. It will be shown that in this geometry at high enough laser intensities the Newton sphere has sufficient symmetry to apply the inverse Abel transformation to reconstruct the three dimensional distribution from the projected ion image. The laser induced controllable alignment was found to have the upper and lower extreme values of 〈P2(cos θ)〉 = 0.7 for the aligned molecule and -0.1 for the anti-aligned molecule, coupled to 〈P4(cos θ)〉 between 0.3 and 0.0. The method to extract the alignment parameters 〈P2(cos θ)〉 and 〈P4(cos θ)〉 directly from the velocity map ion images will be discussed.

Revealing backward rescattering photoelectron interference of molecules in strong infrared laser fields

Photoelectrons ionized from atoms and molecules in a strong laser field are either emitted directly or rescattered by the nucleus, both of which can serve as efficiently useful tools for molecular orbital imaging. We measure the photoelectron angular distributions of molecules (N2, O2 and CO2) ionized by infrared laser pulses (1320 nm, 0.2 ~ 1 × 10(14) W/cm(2)) from multiphoton to tunneling regime and observe an enhancement of interference stripes in the tunneling regime. Using a semiclassical rescattering model with implementing the interference effect, we show that the enhancement arises from the sub-laser-cycle holographic interference of the contributions of the back-rescattering and the non-rescattering electron trajectory. It is shown that the low-energy backscattering photoelectron interference patterns have encoded the structural information of the molecular initial orbitals and attosecond time-resolved dynamics of photoelectron, opening new paths in high-resolution imaging of sub-Ångström and sub-femtosecond structural dynamics in molecules.

Molecular alignment dependent electron interference in attosecond ultraviolet photoionization

We present molecular photoionization processes by intense attosecond ultraviolet laser pulses from numerical solutions of time-dependent Schrödinger equations. Simulations preformed on a single electron diatomic [Formula: see text] show minima in molecular photoelectron energy spectra resulting from two center interference effects which depend strongly on molecular alignment. We attribute such sensitivity to the spatial orientation asymmetry of the photoionization process from the two nuclei. A similar influence on photoelectron kinetic energies is also presented.

Angular momentum sensitive two-center interference

In quantum mechanics the Young-type double-slit experiment can be performed with electrons either traveling through a double slit or being coherently emitted from two inversion symmetric molecular sites. In the latter one the valence photoionization cross sections of homonuclear diatomic molecules were predicted to oscillate over kinetic energy almost 50 years ago. Beyond the direct proof of the oscillatory behavior of these photoionization cross sections σ, we show that the angular distribution of the emitted electrons reveals hitherto unexplored information on the relative phase shift between the corresponding partial waves through two-center interference patterns.

Frustrated tunnel ionization of noble gas dimers with Rydberg-electron shakeoff by electron charge oscillation

Strong field single ionization of homo- and heteronuclear noble gas dimers with ultrashort infrared laser pulses is experimentally investigated. A pronounced photoelectron yield maximum is found for dimers in the momentum range |p|≤0.1  a.u. which is absent for the corresponding monomer. This yield enhancement can be attributed to a new two-step strong field ionization mechanism active only in the dimers. In the first step, frustrated tunnel ionization at one of the atomic centers populates Rydberg states, which then become ionized in a second step through charge oscillation within the dimer ion core.

Ionization suppression of diatomic molecules in an intense midinfrared laser field

Diatomic molecules (e.g., O(2)) in an 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 atom of Xe, while N(2) behaves like a structureless atom. It is found that the S-matrix theory calculation can reproduce well the experimental observations and unambiguously identifies the significant role of two-center interference effect in the ionization suppression of O(2).

Laser-induced low energy electron diffraction in aligned molecules

We measured the photoelectron spectra and angular distributions of partially aligned N(2), O(2), and CO(2) in the rescattering plateau of above threshold ionization (ATI). The measured ATI electrons have relatively low collision energies (<15 eV). The photoelectron angular distributions (PAD) show clearly species and energy dependence. A simple two-center interference model was not able to consistently retrieve structural properties. We conclude that due to the interplay between the electrons and rescattering potential, the molecular structural information is obscured and cannot be extracted conveniently. However, the sensitivity of the PAD to the scattering potential in laser-induced electron diffraction promises a practical tool for studying electron-ion scattering dynamics.

Direct observation of Young’s double-slit interferences in vibrationally resolved photoionization of diatomic molecules

Vibrationally resolved valence-shell photoionization spectra of H₂, N₂ and CO have been measured in the photon energy range 20–300 eV using third-generation synchrotron radiation. Young’s double-slit interferences lead to oscillations in the corresponding vibrational ratios, showing that the molecules behave as two-center electron-wave emitters and that the associated interferences leave their trace in the angle-integrated photoionization cross section. In contrast to previous work, the oscillations are directly observable in the experiment, thereby removing any possible ambiguity related to the introduction of external parameters or fitting functions. A straightforward extension of an original idea proposed by Cohen and Fano [Cohen HD, Fano U (1966) Phys Rev 150:30] confirms this interpretation and shows that it is also valid for diatomic heteronuclear molecules. Results of accurate theoretical calculations are in excellent agreement with the experimental findings.

Extracting electron-ion differential scattering cross sections for partially aligned molecules by laser-induced rescattering photoelectron spectroscopy

We extract large-angle elastic differential cross sections (DCSs) for electrons scattering from partially aligned O2+ and CO2+ molecules using rescattering photoelectrons generated by infrared laser pulses. The extracted DCSs are in good agreement with those calculated theoretically, demonstrating that accurate DCSs for electron-ion scattering can be extracted from the laser-induced rescattering spectra, thus paving the way for dynamic imaging of chemical reactions by rescattering photoelectron spectroscopy.

Structure effects in angle-resolved high-order above-threshold ionization of molecules

We present energy-resolved angular distributions of photoelectrons generated in above-threshold ionization (ATI) of nonaligned diatomic molecules N2 and O2 in high-intensity short laser pulses, with emphasis on the most energetic part of the spectra. The angular distribution for photoelectrons with energy of 10U(p) (U(p): ponderomotive energy), i.e., the plateau cutoff in ATI spectra, is found to be broader in O2 than in N2. Resorting to the analyses from both an S-matrix theory and an intuitive semiclassical model, we attribute the observation to the effect of the ground state molecular orbital structure on high-energy electron emission in strong-field molecular ionization.