Rescattering processes for elliptical polarization: A quantum trajectory analysis

Quantum mechanical modeling of high-intensity laser pulse interaction with hydrogen atom with considering the magnetic field and polarization

In the study of the non-relativistic interaction between high-intensity femtosecond laser pulses and atoms, the influence of the magnetic field is commonly overlooked. This work investigates the effects of the magnetic field in the high-intensity few-cycle laser pulses with non-relativistic intensity of 3.5 × 10 14 W / cm 2 at the center wavelength of 800 nm on the high-order harmonic generation (HHG), attosecond pulse train (APT), isolated attosecond pulse (IAP), and the electron trajectory in the hydrogen atom, employing the numerical solution of the time-dependent Schrödinger equation in three dimensions (3D-TDSE). Two polarizations, linear and circular, are considered. A comparison with the scenario where the magnetic field is not considered shows that the magnetic field can apply significant corrections to the results. Particularly, considering the magnetic field for circular polarization can make the cutoff frequency of HHG coincide with the semi-classical relationship of ħ ω c = I p + 3.17 U p , a case that for circular polarization does not exist without considering the magnetic field. Moreover, accounting for the magnetic field leads to a reduction in the attosecond pulse duration for circular polarization for APT ( 360 as versus 241 as ) and for IAP ( 834 as versus 602 as ). Additionally, the difference in production efficiency of HHG and APT between linear and circular polarization is reduced by two orders of magnitude, when magnetic field is considered. Although considering the magnetic field complicates the electron trajectory, especially for circular polarization, however, our quantum model provides enhanced insight into how the interaction works, especially when and where the electron collides with the parent nucleus. In this case, the quantum mechanical modeling largely covers the huge difference of not considering the magnetic field in the results predicted by other works.

Nondipole effects in terahetz-pulse-assisted strong-field ionization

Nondipole effects in processes assisted by a THz field having the strength of a few MV/cm can be significant due to its long wavelength. We illustrate this for strong-laser-field-induced ionization assisted by a THz field. To this end, we generalize our strong-field-approximation theory so that it includes the first-order term in a 1/c expansion of the vector potential. We show that in this case, in addition to a shift of the maximum of the photoelectron momentum distribution, the differential ionization probability as well as the cutoff energy can be significantly increased. For an explanation of these unexpected results we use the saddle-point method adjusted to include nondipole effects.

Ultraviolet supercontinuum generation driven by ionic coherence in a strong laser field

Supercontinuum (SC) light sources hold versatile applications in many fields ranging from imaging microscopic structural dynamics to achieving frequency comb metrology. Although such broadband light sources are readily accessible in the visible and near infrared regime, the ultraviolet (UV) extension of SC spectrum is still challenging. Here, we demonstrate that the joint contribution of strong field ionization and quantum resonance leads to the unexpected UV continuum radiation spanning the 100 nm bandwidth in molecular nitrogen ions. Quantum coherences in a bunch of ionic levels are found to be created by dynamic Stark-assisted multiphoton resonances following tunneling ionization. We show that the dynamical evolution of the coherence-enhanced polarization wave gives rise to laser-assisted continuum emission inside the laser field and free-induction decay after the laser field, which jointly contribute to the SC generation together with fifth harmonics. As proof of principle, we also show the application of the SC radiation in the absorption spectroscopy. This work offers an alternative scheme for constructing exotic SC sources, and opens up the territory of ionic quantum optics in the strong-field regime.

Strong-laser-field-induced ionization assisted by a terahertz pulse

Extreme terahertz (THz) pulses can be generated via interaction of strong infrared ultrashort laser pulses with a suitable target. Inverting this scheme, we propose to use such THz pulses to control strong-laser-field-driven processes. In particular, we show that for THz-pulse-assisted strong-laser-field ionization the electron yield can be increased by one order of magnitude for some energies, and that the maximal emitted photoelectron energy can be a few times higher than that realized with the laser field alone. This can be achieved with the THz field intensity many orders of magnitude lower than that of the ionizing laser field. The only requirement is that the vector potential amplitude of the THz field, which governs the electron dynamics after the ionization by the laser field, be comparable with that of the used laser field. An important control parameter is the time delay between the THz pulse and the laser pulse. Strong-field ionization of Cs atoms is used for an illustration. The numerical results are obtained applying the improved strong-field approximation. For a physical explanation, we use quantum-orbit theory supported by the modified saddle-point method, as well as a classical model.

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.

Generation of two successive attosecond pulses in separate spectral domains

We demonstrate that two different single attosecond pulses (SAP) can be obtained from naturally separated spectral domains formed during high-order harmonic generation and propagation in a gas medium. We propose a feasible experimental configuration in which one can obtain an SAP in a lower energy domain (<300 eV), or another SAP in a higher energy domain (>300 eV). Without filtering, a double attosecond pulse emission with fixed temporal separation is obtained. The gap between the two spectral domains is close to the onset of the water window.

Gouy's Phase Anomaly in Electron Waves Produced by Strong-Field Ionization

Ionization of atoms by strong laser fields produces photoelectron momentum distributions that exhibit modulations due to the interference of outgoing electron trajectories. For a faithful modeling, it is essential to include previously overlooked phase shifts occurring when trajectories pass through focal points. Such phase shifts are known as Gouy's phase anomaly in optics or as Maslov phases in semiclassical theory. Because of Coulomb focusing in three dimensions, one out of two trajectories in photoelectron holography goes through a focal point as it crosses the symmetry axis in momentum space. In addition, there exist observable Maslov phases already in two dimensions. Clustering algorithms enable us to implement a semiclassical model with the correct preexponential factor that affects both the weight and the phase of each trajectory. We also derive a simple rule to relate two-dimensional and three-dimensional models for linear polarization. It explains the shifted interference fringes and weaker high-energy yield in three dimensions. The results are in excellent agreement with solutions of the time-dependent Schrödinger equation.

Deep Learning for Feynman's Path Integral in Strong-Field Time-Dependent Dynamics

Feynman's path integral approach is to sum over all possible spatiotemporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in the classical view. However, the complete characterization of the quantum wave function with infinite paths is a formidable challenge, which greatly limits the application potential, especially in the strong-field physics and attosecond science. Instead of brute-force tracking every path one by one, here we propose a deep-learning-performed strong-field Feynman's formulation with a preclassification scheme that can predict directly the final results only with data of initial conditions, so as to attack unsurmountable tasks by existing strong-field methods and explore new physics. Our results build a bridge between deep learning and strong-field physics through Feynman's path integral, which would boost applications of deep learning to study the ultrafast time-dependent dynamics in strong-field physics and attosecond science and shed new light on the quantum-classical correspondence.

Symphony on strong field approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics

The strong ellipticity dependence of high-harmonic generation (HHG) in gases enables numerous experimental techniques that are nowadays routinely used, for instance, to create isolated attosecond pulses. Extending such techniques to solids requires a fundamental understanding of the microscopic mechanism of HHG. Here we use first-principles simulations within a time-dependent density-functional framework and show how intraband and interband mechanisms are strongly and differently affected by the ellipticity of the driving laser field. The complex interplay between intraband and interband effects can be used to tune and improve harmonic emission in solids. In particular, we show that the high-harmonic plateau can be extended by as much as 30% using a finite ellipticity of the driving field. We furthermore demonstrate the possibility to generate, from single circularly polarized drivers, circularly polarized harmonics. Our work shows that ellipticity provides an additional knob to experimentally optimize HHG in solids.The mechanisms of high-order harmonic generation in bulk system and dilute gas are different. Here the authors use first-principle methods to explore the ellipticity dependence and control of the HHG in periodic solids by involving the interband and intraband dynamics in Si and MgO.

Electron rescattering in a bicircular laser field

Above-threshold ionization of rare-gas atoms by a bicircular field with its two components counterrotating is theoretically investigated by means of the improved strong-field approximation. Both direct and rescattered electrons are considered and the quantum orbits that lead into a specific final state are calculated and depicted. The angle-dependent spectrum reflects the discrete rotational symmetry of the bicircular field. The backward-scattering contributions are very similar to those generated by a linearly polarized field; several such contributions are rotated one versus the other by the symmetry angle of the discrete rotational symmetry. The forward-scattering contributions dramatically affect the velocity map at comparatively low momenta. The direct-electron spectrum observes reflection symmetry about several symmetry axes determined by the field symmetry. This is broken by rescattering.

Quantum control of electron wave packet during high harmonic process of H2(+) in a combination of a circularly polarized laser field and a Terahertz field

By solving a two-dimensional time-dependent Schrödinger equation we investigate high harmonic generation (HHG) and isolated attosecond pulse generation for the H2+ molecular ion in a circularly polarized laser pulse combined with a Terahertz (THz) field. The harmonic intensity can be greatly enhanced and a continuum spectrum can be obtained when a THz field is added. The HHG process is studied by the semi-classical three-step model and the time-frequency analysis. Our studies show that only short trajectories contribute to HHG. Furthermore, we present the temporal evolution of the probability density of electron wave packet, which perfectly shows a clear picture of the electron's two-time recombination when a THz field is added, and it is the main mechanism of HHG. By superposing the harmonics in the range of 216-249 eV, an isolated attosecond pulse with a duration of about 69 attoseconds can be generated.

Extended virtual detector theory for strong-field atomic ionization

For time-dependent strong-field atomic ionization a new theoretical approach is described that combines the numerical time-dependent Schrödinger equation (TDSE) and the numerical time-dependent Newtonian equation (TDNE). This approach keeps both the accuracy of quantum calculations and the speed of classical calculations. It does not use approximate tunneling formulas. It is applied to a recent experimental result, and we show its successful comparison to extensive TDSE calculations made under exactly the same conditions.

Quantum-orbit analysis for yield and ellipticity of high order harmonic generation with elliptically polarized laser field

We perform a quantum-orbit analysis for the dependence of high-order-harmonic yield on the driving field ellipticity and the polarization properties of the generated high harmonics. The electron trajectories responsible for the emission of particular harmonics are identified. It is found that, in elliptically polarized driving field, the electrons have ellipticity-dependent initial velocities, which lead to the decrease of the ionization rate. Thus the harmonic yield steeply decreases with laser ellipticity. Besides, we show that the polarization properties of the harmonics are related to the complex momenta of the electron. The physical origin of the harmonic ellipticity is interpreted as the consequence of quantum-mechanical uncertainty of the electron momentum. Our results are verified with the experimental results as well as the numerical solutions of the time dependent Schrödinger equation from the literature.

Elliptical polarization favors long quantum orbits in high-order above-threshold ionization of noble gases

We demonstrate the significant role of long quantum orbits in strong-field atomic processes by investigating experimentally and theoretically the above-threshold ionization spectra of noble gases in intense elliptically polarized laser pulses. With increasing laser ellipticity, the yields of different energy regions of the measured electron spectrum in high-order above-threshold ionization drop at different rates. The experimental features can be reproduced by a theoretical simulation based on quantum-orbit theory, revealing that increasing ellipticity favors the contributions of the long quantum orbits in the high-order above-threshold ionization process.

Recollision dynamics and phase diagram for nonsequential double ionization with circularly polarized laser fields

A semiclassical quasistatic model is used to investigate the recollision dynamics in circularly polarized laser fields. A velocity window for recollision to occur is found. Only when the return electron's orbits are irregular does significant double ionization take place. The model reproduces the experimental results for magnesium and explains the apparently conflicting experimental results in terms of an analytical formula that demarcates the phase diagram for the nonsequential double ionization in circularly polarized laser fields.

Experimental study of photodetachment in a strong laser field of circular polarization

Negative fluorine ions are exposed to a circularly polarized infrared laser pulse with a peak intensity on the order of 2.6 x 10(13) W/cm(2). A fundamental difference, as compared to the case of linearly polarized field, is found in the absence of any structure in the photoelectron spectrum that can be associated with the quantum interference effect. This observation is in accord with our recent predictions [S. Beiser, Phys. Rev. A 70, 011402 (2004)10.1103/Phys. Rev. A.70. 011402]. The experiment reveals that the length gauge is appropriate for the description of the field interaction in the frame of the strong field approximation.

Rescattering double ionization of D2 and H2 by intense laser pulses

We have measured momentum spectra and branching ratios of charged ionic fragments emitted in the double ionization of D2 (and H2) molecules by short intense laser pulses. We find high-energy coincident D+ (and H+) ion pairs with kinetic energy releases between 8 and 19 eV which appear for linearly polarized light but are absent for circularly polarized light. The dependence on the polarization, the energy distributions of the ions, and the dependence on laser intensity of yield ratios lead us to interpret these ion pairs as due to a rescattering mechanism for the double ionization. A quantitative model is presented which accounts for the major features of the data.

Photodetachment of H- in a strong infrared laser field

Negative hydrogen ions are exposed to a short infrared laser pulse of 2.15 microm wavelength and 250 fs duration. An imaging technique is used to record the energy resolved angular distribution of photoelectrons. The energy spectrum reveals at least three excess photon detachment channels. A quantum interference effect, resulting in an unusual dependence of the angular distribution on the electron kinetic energy, is most prominent in the lowest two-photon detachment channel. The appearance of this effect is discussed in terms of the threshold law of photodetachment.

Threshold effects on angular distributions for multiphoton detachment by intense elliptically polarized light

Unusual threshold effects are found theoretically in the frequency and intensity dependence of angular distributions produced by an elliptically polarized laser as well as in the elliptic dichroism parameter, which measures the asymmetry of the angular distribution.

Feynman's path-integral approach for intense-laser-atom interactions

Atoms interacting with intense laser fields can emit electrons and photons of very high energies. An intuitive and quantitative explanation of these highly nonlinear processes can be found in terms of a generalization of classical Newtonian particle trajectories, the so-called quantum orbits. Very few quantum orbits are necessary to reproduce the experimental results. These orbits are clearly identified, thus opening the way for an efficient control as well as previously unknown applications of these processes.

Above-threshold ionization by an elliptically polarized field: interplay between electronic quantum trajectories

Measurements of energy-resolved angular distributions of electrons generated in above-threshold ionization of rare gases in a field with elliptical polarization are presented, with emphasis on the high-energy part of the spectra. The data show a second plateau at a specific angle with respect to the large component of the laser field. The results are compared to a calculation based on a strong-field rescattering approximation. This is interpreted in terms of the superposition of quantum trajectories. The second plateau is associated with the interference of electrons that do and that do not rescatter.