Photoelectron Momentum Distributions Research Articles

Modulation of H atom photoelectron momentum distribution by chirped laser pulses of different wavelengths

The wavelength dependence of the holographic interference structure in the photoelectron momentum distribution (PMD) of hydrogen atoms under a few-cycle chirped laser field is investigated using a two-dimensional (2D) semiclassical two-step (SCTS) model. Under the constraint of a fixed chirp parameter, we observe an amplification in the impact of the chirp parameter on the laser field waveform as the wavelength increases. This enhancement facilitates effective modulation of the ionization time window. As the wavelength reaches a certain threshold, the double-slit interference pattern undergoes an observable expansion towards the left. Furthermore, based on the variations in X-axis momentum (Px) concerning ionization time at different wavelengths and the corresponding distribution of classical electron trajectories at those wavelengths, we present a more comprehensive explanation for the expansion of interference patterns. This expansion can be attributed to changes in wavelength, which result in modifications to the laser field’s waveform, consequently leading to a significant acceleration of ionized electrons when exposed to chirped laser pulses. It is worth noting that by tuning the negative chirp parameter, the leftward expansion of the double-slit interference pattern can also be achieved, particularly when shorter wavelengths of chirped laser pulses are employed.

Enhancement and suppression of nonsequential double ionization by spatially inhomogeneous fields

Using the three-dimensional classical ensemble approach, we theoretically investigate the nonsequential double ionization of argon atoms in an intense laser field enhanced by bowtie-nanotip. We observe an anomalous decrease in the double ionization yield as the laser intensity increases, along with a significant gap in the low momentum of photoelectrons. According to our theoretical analysis, the finite range of the induced field by the nanostructure is the fundamental cause of the decline in double ionization yield. Driven by the enhanced inhomogeneous field, energetic electrons can escape from the finite range of nanotips without returning. This reduces the possibility of re-scattering on the nucleus and imprints the finite size effect into the double ionization yield and momentum distribution of photoelectrons in the form of yield decline and a gap in the photoelectron-momentum distribution.

Response time of an electron inside a molecule to light in strong-field ionization.

We study ionization of aligned H2+ 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 which is encoded in the offset angle and is manifested as the time spent in tunneling ionization, is about 15 attoseconds longer for the molecule than the atom. This time difference is further enlarged when increasing the internuclear distance of the molecule.

Convolutional neural network for retrieval of the time-dependent bond length in a molecule from photoelectron momentum distributions

Abstract We apply deep learning for retrieval of the time-dependent bond length in the dissociating two-dimensional H2 + molecule using photoelectron momentum distributions. We consider a pump-probe scheme and calculate electron momentum distributions from strong-field ionization by treating the motion of the nuclei classically, semiclassically or quantum mechanically. A convolutional neural network trained on momentum distributions obtained at fixed internuclear distances retrieves the time-varying bond length with an absolute error of 0.2-0.3 a.u.

Photoelectron jets and interference structures in ionization beyond dipole approximation: carrier- envelope phase effects and vortex streets.

We have analyzed photoelectron jet formation in strong-field ionization using the hydrodynamic picture of quantum mechanics. We showed that von-Kármán-like vortex streets emerge in between jets in photoelectron momentum distributions. The spatial orientation of the jets can be controlled by tailoring the carrier-envelope phase of the driving laser pulse. This indicates that it is possible to experimentally measure emitted photoelectrons off the optical axis, which opens up new possibilities for high-frequency laser pulse diagnostics.

Control of Frustrated Nonsequential Double Ionization Channels With the Carrier-Envelope Phase of Elliptically Polarized Laser Pulses

Abstract Using a classical approach, we theoretically investigate the frustrated double ionization (FDI) of Ar atoms under elliptically polarized (EP) laser fields. The FDI yield is calculated as a function of laser intensity with different carrier-envelope phases (CEPs), and, similar to the carrier-envelope phase (CEP) dependence of nonsequential double ionization (NSDI), several knee-shaped structures appear. Moreover, both recollision and direct ionization trajectories are observed in FDI events for the “knee” structure regime. The footprints of which channel leads to FDI are encoded in the photoelectron momentum distributions. FDI events related to recollision excitation with subsequent ionization channels and recollision impact ionization channels can be controlled by CEP in EP laser fields.

Control of the spider-like interference structure in photoelectron momentum distributions of a helium atom in a few-cycle nonlinear chirped laser pulse.

We investigate theoretically the photoelectron momentum distributions (PMDs) of the helium atom in the few-cycle nonlinear chirped laser pulse. The numerical results show that the direction of the spider-like interference structure in PMDs exhibits periodic variations with the increase of the chirp parameter. It is illustrated that the direction of the spider-like interference structure is related to the direction of the electron motion by tracking the trajectories of the electrons. We also demonstrate that the carrier-envelope phase can precisely control the opening of the ionization channel. In addition, we investigate the PMDs when a chirp-free second harmonic (SH) laser pulse is added to the chirped laser field, the numerical results show that the interference patterns can change from only spider-like interference structure to both spider-like and ring-like interference structures.

High-order above-threshold ionisation of diatomic molecules by few-cycle bicircular and orthogonally polarised two-colour pulses.

Improved molecular strong-field approximation theory is used to calculate the ionisation probability for the high-order above-threshold ionisation process induced by a few-cycle pulse with two carrier frequencies and one envelope. The asymmetry in the photoelectron momentum distribution is due to the ultrashort nature of the driving pulse and due to the relative orientation of the molecule with respect to the laser field. We introduce the generalised asymmetry parameter, which can be used to quantitatively measure the asymmetry between the photoelectron spectra along arbitrarily many selected directions. We investigate the difference between the asymmetry parameters calculated for atomic and molecular targets and show that the contributions to the asymmetry strongly depend on the type of the employed driving pulse. For the driving pulse with components that are linearly polarised with mutually orthogonal polarisations, we find that the main source of the asymmetry, especially in the high-energy part of the spectrum, is the ultrashort nature of the pulse. The relative orientation of the molecule with respect to the laser pulse only affects the low- and medium-energy parts of the spectrum. On the other hand, for the driving pulse with circularly polarised counterrotating components, the asymmetry introduced by molecular orientation is more pronounced. We also analyse the influence of the characteristics of molecular orbitals on the asymmetries using the examples of N2 and O2 molecules.

Electron vortex generations in photoionization of hydrogen atoms by circularly-polarized chirped attosecond pulses

By numerically solving the time-dependent Schrödinger equation and employing the analytical perturbative model, we investigated the chirp-induced electron vortex in the photoionization of hydrogen atoms by a pair of counter-rotating circularly polarized chirped attosecond extremely ultraviolet pulses. We demonstrated that single-photon ionization of hydrogen atoms generates photoelectron momentum distributions (PMDs) with distinct helical vortex structures either with or without a time delay between two counter-rotating circularly polarized laser pulses. These structures are highly sensitive to both the time delay between the pulses and their chirp parameters. Our analytical model reveals that the splitting of vortex spirals is caused by the sign changing of the chirp-induced frequency-dependent time delay. We showed that to obtain the counterpart of the PMD under a pair of counter-rotating circularly polarized chirped pulses, both chirp parameters and ordering of pulses need to be reversed.

Probing the electron motion in molecules using forward-scattering photoelectron holography.

Charge migration initiated by the coherent superposition of several electronic states is a basic process in intense laser-matter interactions. Observing this process on its intrinsic timescale is one of the central goals of attosecond science. Here, using forward-scattering photoelectron holography we theoretically demonstrate a scheme to probe the charge migration in molecules. In our scheme, by solving the time-dependent Schrödinger equation, the photoelectron momentum distributions (PEMDs) for strong-field tunneling ionization of the molecule are obtained. For a superposition state, it is shown that an intriguing shift of the holographic interference appears in the PEMDs, when the molecule is aligned perpendicularly to the linearly polarized laser field. With the quantum-orbit analysis, we demonstrate that this shift of the interference fringes is caused by the time evolution of the non-stationary superposition state. By analyzing the dependence of the shift on the final parallel momentum of the electrons, the relative phase and the expansion coefficient ratio of the two electronic states involved in the superposition state are determined accurately. Our study provides an efficient method for probing the charge migration in molecules. It will facilitate the application of the forward-scattering photoelectron holography to survey the electronic dynamics in more complex molecules.

Electron vortices generation of photoelectron of H2+ by counter-rotating circularly polarized attosecond pulses

Molecular-frame photoelectron momentum distributions (MF-PMDs) of an H2+ molecule ion in the presence of a pair of counter-rotating circularly polarized attosecond extreme ultraviolet laser pulses is studied by numerically solving the two-dimensional time-dependent Schrödinger equation within the frozen-nuclei approximation. At small time delay, our simulations show that the electron vortex structure is sensitive to the time delay and relative phase between the counter-rotating pulses when they are partially overlapped. By adjusting time delay and relative phase, we have the ability to manipulate the MF-PMDs and the appearance of spiral arms. We further show that the internuclear distance can affect the spiral vortices due to its different transition cross sections in the parallel and perpendicular geometries. The lowest-order perturbation theory is employed to interpret these phenomena qualitatively. It is concluded that the internuclear distance-dependent transition cross sections and the confinement effect in diatomic molecules are responsible for the variation of vortex structures in the MF-PMDs.

Generation of Ultrafast Attosecond Magnetic Field from Ne Dimer in Circularly Polarized Laser Pulses

By numerically solving time-dependent Schrödinger equations, we investigate the generation of electron currents, ultrafast magnetic fields and photoelectron momentum distributions (PMD) when circularly polarized laser pulses interact with a Ne dimer in the charge migration (CM) process. By adjusting the laser wavelength, we consider two cases: (i) coherent resonance excitation (λ = 76 nm) and (ii) direct ionization (λ = 38 nm). The results show that the current and magnetic field generated by the Ne dimer under resonance excitation are stronger than under direct ionization. This phenomenon is due to the quantum interference between the initial state 2pσ g and the excited state 3sσ g under resonance excitation, so the CM efficiency of the dimer can be improved and the strength of the PMD under different ionization conditions is opposite to the strength of the electron current and induced magnetic field. In addition, we also find that both 2pπ g and 2pπ u have coherent resonance excitation with 3sσ g state and generate periodic oscillating currents for the Ne dimer. The study of the dynamics of the Ne dimer under different ionization conditions lays a foundation for research of ultrafast magnetism in complex molecular systems.

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.

H2 formation via non-Born-Oppenheimer hydrogen migration in photoionized ethane

Neutral H2 formation via intramolecular hydrogen migration in hydrocarbon molecules plays a vital role in many chemical and biological processes. Here, employing cold target recoil ion momentum spectroscopy (COLTRIMS) and pump-probe technique, we find that the non-adiabatic coupling between the ground and excited ionic states of ethane through conical intersection leads to a significantly high yield of neutral H2 fragment. Based on the analysis of fingerprints that are sensitive to orbital symmetry and electronic state energies in the photoelectron momentum distributions, we tag the initial electronic population of both the ground and excited ionic states and determine the branching ratios of H2 formation channel from those two states. Incorporating theoretical simulation, we established the timescale of the H2 formation to be ~1300 fs. We provide a comprehensive characterization of H2 formation in ionic states of ethane mediated by conical intersection and reveals the significance of non-adiabatic coupling dynamics in the intramolecular hydrogen migration.

Single-photon ionization of aligned H with near-ionization-threshold photon energy

We study single-photon ionization of aligned H in a high-frequency low-intensity laser field. We focus on the cases where the laser frequency is near to or somewhat larger than the ionization potential of the target. The calculated photoelectron momentum distribution through numerical solution of time-dependent Schrödinger equation shows clear interference patterns. However, different from the cases of photon energy far larger than the ionization potential usually explored in experiments, the positions of interference maxima and minima for the present cases can not be explained by the interference of the electronic wave with the observed momentum between these two atomic centers of the molecule. By developing a theory model applicable for ionization of molecules in high-frequency laser field, we show that the Coulomb potential plays an important role in the momentum component of the emitting electronic wave near the nuclei, resulting in a remarkable shift of the interference pattern. A simple expression with Coulomb-modified momentum is obtained to predict the interference extrema, which gives suggestions for probing the structure and electron dynamics of the aligned molecule in single-photon ionization with lower photon energy.

Exchange effects in strong-field ionization of the excited lithium ion induced by one- and two-component laser fields

Spin-dependent effects in strong-laser-field-induced above-threshold ionization of excited Li+ ions, caused by the requirement that the electron wave function is antisymmetric, are analyzed using the strong-field approximation and saddle-point method. For an excited Li+ ion exposed to a linearly polarized laser field, the minima in the photoelectron momentum distribution in the polarization plane appear if the excited Li+ ion state is the spin singlet state, while for the spin triplet state these minima are absent. The difference between the spectra obtained with these spin states is quantified by the corresponding normalized difference of the differential ionization probabilities. Employing the saddle-point method, we show that, for the spin singlet state, all relevant contributions to the differential ionization probability exhibit minima for approximately the same values of the photoelectron energy and emission angle, thus leading to the minima in the total spectra. Similar conclusions hold for a bicircular driving field. In this case, the range of values of the photoelectron energy and emission angle for which different saddle-point contributions exhibit minima is almost the same for all saddle-point solutions. This is particularly true for the high-energy part of the spectrum, and the minima are more pronounced than for the linearly polarized driving field case. In order to check whether these minima can be detected in an experiment, we perform focal averaging, which takes into account the intensity distribution in the laser focus. For both linearly polarized and bicircular driving fields, the minima survive the focal-averaging procedure. They are slightly blurred in the former case, while in the latter case the focal averaging almost does not affect the minima at all. Finally, we confirm that similar conclusions hold for the photoelectron velocity maps in the plane that contains the laser-field propagation direction.

Strong-Field Ionization of Hydrogen Atoms with Quantum Light.

We study the strong-field ionization driven by quantum lights. Developing a quantum-optical-corrected strong-field approximation model, we simulate the photoelectron momentum distribution with squeezed-state light, which manifests as notably different interference structures from that with coherent-state (classical) light. With the saddle-point method, we analyze the electron dynamics and reveal that the photon statistics of squeezed-state light fields endows the tunneling electron wave packets with a time-varying phase uncertainty and modulates the photoelectron intracycle and intercycle interferences. Moreover, it is found the fluctuation of quantum light imprints significant influence on the propagation of tunneling electron wave packets, in which the ionization probability of electrons is considerably modified in time domain.

Two-color attosecond chronoscope.

We study ionization of atoms in strong orthogonal two-color (OTC) laser fields numerically and analytically. The calculated photoelectron momentum distribution shows two typical structures: a rectangular-like one and a shoulder-like one, the positions of which depend on the laser parameters. Using a strong-field model which allows us to quantitatively evaluate the Coulomb effect, we show that these two structures arise from attosecond response of electron inside an atom to light in OTC-induced photoemission. Some simple mappings between the locations of these structures and response time are derived. Through these mappings, we are able to establish a two-color attosecond chronoscope for timing electron emission, which is essential for OTC-based precise manipulation.

Adiabatic theory of generation and rescattering of vortex electrons in strong-field ionization by elliptically polarized pulses

The adiabatic theory of strong-field ionization is extended to the specific configuration in which ionization occurs from a vortex orbital in an axially symmetric target by an elliptically polarized pulse with small ellipticity and the major axis of the polarization ellipse directed along the vortex axis of the initial state. Generation of vortex electrons in the continuum, their propagation in the laser field, and subsequent rescattering on the parent ion are described. Adiabatic asymptotics of the rescattering parts of the solution to the time-dependent Schr\"odinger equation and the ionization amplitude are obtained. On the basis of these results, the factorization formula giving the photoelectron momentum distribution (PEMD) in the vicinity of a backward rescattering caustic is derived. Our interest in the present configuration stems from the fact that, because of the nonzero ellipticity of the field, liberated vortex electrons arrive for rescattering with a nonzero impact parameter. The corresponding scattering amplitude generalizes the recently introduced vortex scattering amplitude characterizing head-on vortex-target rescattering in the linear polarization case [O. I. Tolstikhin and T. Morishita, Phys. Rev. A 99, 063415 (2019)]. Using the factorization formula, one can extract the absolute value of this generalized scattering amplitude from the observable PEMD, which opens a new window for target structure imaging in strong-field physics. The theory is illustrated by calculations for two atomic targets, ${\mathrm{He}}^{+}(2p,m=1)$ and $\mathrm{Xe}(5p,m=1)$. We show that in the case of the initial $\ensuremath{\pi}$ orbital and nonzero ellipticity not only the absolute values of two head-on scattering amplitudes with $m=0$ and 1, but also their phase difference as functions of the scattering angle can be extracted from the PEMD.

Strong-field nonsequential double photoionization using virtual-detector theory with path summation

We present an ab initio study of the nonsequential strong-field ionization dynamics of a model two-electron atom with helium character. Single- and double-ionization events are characterized and displayed using detector signals extracted at different points in the two-electron two-dimensional space. The double photoelectron momentum distribution is calculated via coherent path-summation over virtual-particle trajectories. A comparison is made between the momentum distributions obtained with the virtual-detector method, the Schr\"odinger wave function, and the time-dependent surface flux method developed by Tao and Scrinzi [New J. Phys. 14, 013021 (2012)]. Insights into different ionization and electron recollision pathways are gained from detailed virtual-particle tracking and energy-time readouts. This study demonstrates the extension of virtual-detector theory to strong-field multielectron quantum dynamics and highlights the importance of the evolving quantum phase in quasiclassical electron propagation.