Above-threshold Ionization Process Research Articles

Polarization control of above-threshold ionization spectrum in elliptically polarized two-color laser fields

We study the above-threshold ionization (ATI) process of atoms exposed to fundamental and high-frequency lasers with arbitrary ellipticity by applying the frequency-domain theory. It is found that the angular-resolved ATI spectrum is sensitive to ellipticities of two lasers and emitted angles of the photoelectron. Particularly for the photon energy of the high-frequency laser more than atomic ionization potential, the width of plateau tends to a constant with increasing ellipticity of fundamental field, the dip structure disappears with increasing ellipticity of the high-frequency field. With the help of the quantum channel analysis, it is shown that the angular distribution depends mainly on the ellipticity of high-frequency field in the case that its frequency is high. Moreover, one can see that the maximal and minimal energies in quantum numerical results are in good agreement with the classical prediction. Our investigation may provide theoretical support for experimental research on polarization control of ionization in elliptically polarized two-color laser fields.

Spectral phase effects in above threshold ionization

We present theoretical studies of above threshold ionization (ATI) using sculpted laser pulses. The time-dependent Schrödinger equation is solved to calculate the ATI energy and momentum spectra, and a qualitative understanding of the electron motion after ionization is explored using the simple man’s model and a classical model that solves Newton’s equation of motion. Results are presented for Gaussian and Airy laser pulses with identical power spectra, but differing spectral phases. The simulations show that the third order spectral phase of the Airy pulse, which can alter the temporal envelope of the electric field, causes changes to the timing of ionization and the dynamics of the rescattering process. Specifically, the use of Airy pulses in the ATI process results in a shift of the Keldysh plateau cutoff to lower energy due to a decreased pondermotive energy of the electron in the laser field, and the side lobes of the Airy laser pulse change the number and timing of rescattering events. This translates into changes to the high-order ATI plateau and intra- and intercycle interference features. Our results also show that laser pulses with identical carrier envelope phases and nearly identical envelopes yield different photoelectron momentum distributions, which are a direct result of the pulse’s spectral phase.

Light-matter entanglement after above-threshold ionization processes in atoms

Light-matter entanglement plays a fundamental role in many applications of quantum information science. Thus, finding processes where it can be observed is an important task. Here, using a one-dimensional model, we address this matter by investigating theoretically the entanglement between light and electrons generated in the above-threshold ionization (ATI) process. The study is based on the backaction of the ATI process on the quantum optical state of the system, and its dependence on the kinetic energy and direction of the emitted photoelectrons. Taking into account the dynamics of the process, we demonstrate the creation of hybrid entangled states. The amount of entanglement has been studied in terms of the entropy of entanglement. Additionally, we use the Wigner function of the driving field mode to motivate the entanglement characterization when considering electrons propagating in opposite directions.

Photoionization of Electrons in Degenerate Energy Level of Hydrogen Atom Induced by Strong Laser Pulses

Photoionization dynamics of bounded electrons in the ground state, the first and second excited states of a hydrogen atom, triggered by ultrashort near-infrared laser pulses, have been investigated in a transition regime (γ∼1) that offers both multiphoton and tunneling features. Significant differences in spectral characteristics are found between the three low-energy states. The H(2s) ionization probability is larger than the H(2p) value with a special oscillating structure, but both are much greater than the ground state H(1s) in a wide range of laser intensities. By comparing the momentum spectrum and angular distributions of low-energy photoelectrons released from these degenerate states, we find the H(2p) state shows a stronger long-range Coulomb attraction force than the H(2s) state on account of the difference in the initial electron wave packet. Furthermore, analysis of the photoelectron momentum distributions sheds light on both the first and second excited states with a symmetrical intercycle interference structure in a multicycle field but an intracycle interference of an asymmetric left-handed or right-handed rotating spectrum in a few-cycle field. By analyzing photoelectron spectroscopy, we identify the parity characteristics of photoelectrons in different energy intervals and their corresponding above-threshold single-photon ionization (ATSI) or above-threshold double-photon ionization (ATDI) processes. We finally present the momentum distributions of the electrons ionized by laser pulses with different profiles and find the carrier-envelope phase (CEP) is a strong factor in deciding the rotating structure of the emission spectrum, which provides a new method to distinguish the CEP of few-cycle pulses.

Identification of Above-Threshold Ionization by Imaging Photoelectrons from Ammonia Molecules in an Intense Femtosecond Laser Field

The above-threshold ionization process of ammonia molecules induced by a femtosecond laser field at 800 nm is studied in the intensity range from 1.6 × 1013 to 5.7 × 1013 W/cm2. Channel switching under different laser intensities is observed and identified in the photoelectron kinetic energy spectra of ammonia. Based on the photoelectron kinetic energy distributions and the photoelectron angular distributions, the characteristic peaks observed are exclusively assigned to the multiphoton resonance through certain intermediate states, followed by multiphoton above-threshold ionization.

Influence of polarization directions of the IR+XUV two-color laser fields on angle-resolved photoelectron energy spectrum.

By employing the frequency-domain theory, we investigate the influence of polarization directions on angle-resolved photoelectron energy spectrum in the above-threshold ionization (ATI) process of atoms exposed to the IR+XUV two-color laser fields, which shows the multiplateau structures. When the ionized electron is emitted along the IR laser's polarization direction, the width of each plateau keeps a certain energy range, and the jet structures and main lobes are determined by both the emission angle relative to the polarization direction of the XUV laser field and the number of the XUV photons absorbed by the electron. While when the ionized electron is emitted along the XUV laser's polarization direction, the width of each plateau depends on the polarization direction of the IR laser field, and the angular distribution of the ionized electron exhibits the isotropic characteristics. These results show that the ATI spectrum may be effectively controlled by changing the angle between the two laser fields' polarization directions.

Laser-induced processes with homonuclear diatomic molecules in orthogonally polarized two-color laser field

Using our theory which is based on the strong-field approximation we analyze high-order above-threshold ionization and high-order harmonic generation processes for the case of the homonuclear diatomic molecules exposed to an orthogonally polarized two-color (OTC) laser field. The OTC field represents a superposition of two linearly polarized fields with mutually orthogonal polarizations and different frequencies. We analyze the photoelectron energy spectra and the harmonic ellipticity as a function of the ratio of the intensities of the OTC laser-field components and the relative phase. Some combinations of the values of these parameters lead to the high-energy electrons, while the harmonic ellipticity depends strongly on the ratio of the intensities of the laser-field components. It is possible to find the value of this ratio for which the ellipticity of the emitted harmonics is large. The signes of ellipticity are opposite for the molecular orientations which are connected through the reflection with respect to the axis along the first OTC field component. This symmetry is explained using the expression which relates the T-matrix element and the harmonic ellipticity.

Rescattering time-energy analysis of high-order above-threshold ionization in few-cycle laser fields

A Wigner distributionlike function based on the improved strong-field approximation theory is proposed to calculate the rescattering time-energy distribution (RTED) of high-energy photoelectrons of atomic above-threshold ionization process in few-cycle laser fields with different frequencies. The RTED shows bell-like stripes and the outermost stripe is compared with semiclassical results given by the simple-man model with consideration of different positions of tunnel exit and different initial longitudinal momenta. Analysis indicates the existence of the tunnel exit. However, though it shifts farther away from the core with decreasing frequency, the position of the tunnel exit is significantly less than the prediction by adiabatic theory even for the low-frequency case which is well in the tunneling regime. Our results also imply that the effect of the tunnel exit is more important than that of the initial longitudinal momentum at the tunnel exit for the backward-scattering electrons. Moreover, the inner stripe structures in the RTED are attributed to interference between electrons with the same final energy emitted at different ionization times.

Asymmetric structure of atomic above-threshold ionization spectrum in two-color elliptically polarized laser fields**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474348, 11674198, 11425414, and 11774411).

According to the frequency-domain theory, we investigate the asymmetric structure of above-threshold ionization (ATI) spectrum of an atom in two-color elliptically polarized (EP) laser fields. When both laser fields are linearly polarized (LP), the spectrum shows that the multi-plateau structure is symmetric about the emitted angle of electron at π/2, while the spectrum becomes asymmetric and shifts rightwards with the increase of the EP degree of the IR laser field. Since the total ATI process is regarded as including direct ATI and the rescattering ATI, we analyze the spectrum structure of direct ATI and rescattering ATI separately. Using the saddle-point approximation, we find that for direct ATI, the fringes on the spectrum are mainly attributed to the fact that the ionization probability becomes very small when the direction of emitted electrons is perpendicular to the direction of the XUV laser polarization; while for the rescattering ATI, the interference fringes on the spectrum mainly come from the superposition of the waist structures on the spectra of all sub-channels.

Vibrationally resolved above-threshold ionization in NO molecules by intense ultrafast two-color laser pulses: An experimental and theoretical study

We present above-threshold ionization (ATI) in the molecule nitric oxide, NO, by intense (${10}^{12}--{10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$) two-color femtosecond laser pulses. Vibrationally resolved coherent interference phenomena of multiphoton and multipathway ionization processes have been investigated by measuring experimentally and modeling theoretically the molecular photoionization yields. We find that the ATI photoelectron distribution of NO, initiated from degenerate electronic and vibrational states, depends on the relative phase of the two pulses, the kinetic energy, and emission angle of the photoelectrons. This dependence codes the information of interference effects of molecular electronic states. AC Stark effects modulate interference patterns in ATI spectra. Moreover, the ATI spectra exhibit peak energy dependencies that illustrate interference effects from coherent couplings between various ionization channels. These features reflect the molecular property and the multiple channel ionization interference effects in ATI processes. The results allow to explore coherent electron-vibration processes in ultrafast molecular photoionization.

Angular resolved above-threshold ionization spectrum of an atom in IR+XUV orthogonally polarized two-color laser fields.

We investigate the above-threshold ionization (ATI) process of atoms exposed to the IR+XUV orthogonally polarized two-color laser fields by using the frequency-domain theory. It is shown that there exists a dip structure in each plateau of the angular resolved ATI spectrum. The dip structure in the first plateau is attributed to the fact that the electron cannot absorb one XUV photon when its emission direction is perpendicular to the XUV laser polarization, while the one in the second plateau is attributed to the coherent results of different channels. The emergence of dip structure is associated directly with the XUV laser field. Furthermore, by applying the saddle-point approximation, it is found that the fringes on the spectrum is caused by the interference of two trajectories for different saddle-points in the IR laser field. Finally, it is found that, in the high energy region, the probability of ATI spectrum is mainly determined by the XUV laser field, and the width of each plateau is mainly determined by the IR laser field; on the other hand, the ATI spectrum of the low energy region is only determined by the IR laser field.

Angle-resolved photoelectron energy spectrum from the high-order above-threshold ionization process in IR+XUV two-color laser fields

The angle-resolved photoelectron energy spectrum (PES) of high-order above-threshold ionization (HATI) spectrum in IR+XUV two-color laser fields has been investigated. We found that the quantum feature corresponding to the absorption of the XUV photon is well illustrated by a peculiar dip structure in the second plateau of the HATI spectrum. By the channel analysis, we show that the angle-resolved PES is attributed to the coherent summation over contributions of different channels, and the dip structure in the spectrum is directly related to the absorption of one XUV photon of the ionized electron during the laser-assisted collision (LAC) with its parent ion in the two-color laser fields. Moreover, by employing the saddle-point approximation, we obtain the classical energy orbit equation, and find that the dip structure comes from the fact that the LAC is limited at a certain direction by the momentum conservation law as the electron absorbs one XUV photon during the collision, where the probability of the HATI gets its minimum value. Finally, we find that the interference pattern in the whole spectrum is attributed to the interference of different orbits at collision moments t0 and in the LAC process.

Above-threshold ionization of hydrogen atom in chirped laser fields**Project supported by the National Natural Science Foundation of China (Grant Nos. 11664035, 11465016, 11764038, 11364038, and 11564033).

Above-threshold ionization (ATI) of a hydrogen atom exposed to chirped laser fields is investigated theoretically by solving the time-dependent Schrödinger equation. By comparing the energy spectra, the two-dimensional momentum spectra, and the angular distributions of photoelectron for the laser pulses with different chirp rates, we show a very clear chirp dependence both in the multiphoton and tunneling ionization processes but no chirp dependence in the single-photon ionization. We find that the chirp dependence in the multiphoton ionization based ATI can be attributed to the excited bound states. In the single-photon and tunneling ionization regimes, the electron can be removed directly from the ground state and thus the excited states may not be very important. It indicates that the chirp dependence in the tunneling ionization based ATI processes is mainly due to the laser pulses with different chirp rates.

Above-threshold ionization in multicenter molecules: The role of the initial state

A possible route to extract electronic and nuclear dynamics from molecular targets with attosecond temporal and nanometer spatial resolution is to employ recolliding electrons as `probes'. The recollision process in molecules is, however, very challenging to treat using {\it ab initio} approaches. Even for the simplest diatomic systems, such as H$_2$, today's computational capabilities are not enough to give a complete description of the electron and nuclear dynamics initiated by a strong laser field. As a consequence, approximate qualitative descriptions are called to play an important role. In this contribution we extend the work presented in N. Su\'arez {\it et al.}, Phys.~Rev. A {\bf 95}, 033415 (2017), to three-center molecular targets. Additionally, we incorporate a more accurate description of the molecular ground state, employing information extracted from quantum chemistry software packages. This step forward allows us to include, in a detailed way, both the molecular symmetries and nodes present in the high-occupied molecular orbital. We are able to, on the one hand, keep our formulation as analytical as in the case of diatomics, and, on the other hand, to still give a complete description of the underlying physics behind the above-threshold ionization process. The application of our approach to complex multicenter - with more than 3 centers, targets appears to be straightforward.

Nonsequential double ionization of helium in IR+XUV two-color laser fields II: collision-excitation ionization process

We recently investigated the collision-ionization mechanism of the nonsequential double-ionization (NSDI) process in IR+XUV two-color laser fields [(2016) Phys. Rev. A 93 043417]. Here, we extend this work to study the collision-excitation-ionization (CEI) mechanism of the NSDI processes in the two-color laser fields with different laser conditions. It is found that the CEI mechanism makes a dominant contribution to the NSDI as the extreme ultraviolet (XUV) photon energy is smaller than the ionization threshold of the He+ ion, and the momentum spectrum shows complex interference patterns and symmetrical structures. By channel analysis, we find that, as the energy carried by the recollision electron is not enough to excite the bound electron, the bound electron will absorb XUV photons during their collision; as a result, both forward and backward collisions make a comparable contribution to the NSDI processes. However, it is found that, as the energy carried by the recollision electron is large enough to excite the bound electron, the bound electron does not absorb any XUV photon and it is excited only by sharing the energy carried by the recollision electron, hence the forward collision plays a dominant role in the NSDI processes. Moreover, we find that the interference patterns of the NSDI spectra can be reconstructed by the spectra of two above-threshold ionization (ATI) processes, which may be used to analyze the structure of the two separate ATI spectra by NSDI processes.

Role of XUV Photons in Atomic High-Order Above-Threshold Ionization Processes in IR+XUV Two-Color Laser Fields * *Supported by the National Natural Science Foundation of China under Grant Nos 11474348, 61275128, 11274050, 11334009 and 11425414, the NSERC of Canada, the Canadian Computing Facilities of SHARCnet and ACEnet, and the National Basic Research Program of China under Grant No 2013CB922200.

We investigate the above-threshold ionization of an atom in a combined infrared (IR) and extreme ultraviolet (XUV) two-color laser field and focus on the role of XUV field in the high-order above-threshold ionization (HATI) process. It is demonstrated that, in stark contrast to previous studies, the XUV laser may play a significant role in atomic HATI process, and in particular, the XUV laser can accelerate the ionized electron in a quantized way during the collision between the electron and its parent ion. This process cannot be explained by the classical three-step model. Our results indicate that the previously well-established concept that HATI is an elastic recollision process is broken down.

Spin-dependent effects in high-order above-threshold ionization: spin–orbit interaction and exchange effects

Spin-dependent effects in atomic processes can be caused by the spin–orbit interaction or/and by the requirement that the wave function of identical electrons is antisymmetric. Such effects are usually neglected in strong-field physics. We show two examples, supported by theoretical results and numerical calculations, in which these effects are important. The first one is based on strong-field ionization of Xe atoms by a bicircular field. The corresponding momentum distribution of spin-polarized electrons emitted in the above-threshold ionization process exhibits wavelength-dependent fast oscillations. For longer wavelengths and small electron emission angle there is a wide photoelectron kinetic energy region in which the spin asymmetry parameter changes continuously from large positive to large negative values. In addition, the emission time of such electrons in high-order above-threshold ionization is determined on the attosecond time scale. The second process considered is high-order above-threshold ionization of excited Li+ ions. We have found that in this case, even in the absence of spin–orbit coupling, the photoelectron momentum distribution strongly depends on the initial spin state. In the singlet state we have characteristic minima, which are caused by the destructive interference of the direct and exchange rescattering amplitudes. Such minima are absent in the triplet state.

Above-threshold ionization processes in diatomic molecules driven by strong laser fields

SynopsisIn this work we develop a general theory to study above-threshold ionization (ATI) in symmetric diatomic molecules. It is based on the Strong Field Approximation (SFA) and allows us to underpin different physical processes corresponding to (i) direct tunneling ionization; (ii) electron rescattering on the center of origin; and, finally, (iii) electron rescattering on a different center. Very good agreement is observed in comparison of the results obtained with the time-dependent Schrödinger equation (TDSE). Our model also captures the dependence of the ATI spectra on the internuclear distance making possible to retrieve molecular structural information.

Intensity dependence of nonsequential double ionization of helium in IR+XUV two-color laser fields

By applying the frequency-domain theory, we investigate the dependence of momentum spectra on laser intensity in a nonsequential double ionization (NSDI) process of helium in infrared (IR) and extreme ultraviolet (XUV) two-color laser fields. We find that the two-color laser fields play distinct roles in an NSDI process, where the IR laser field mainly determines the width of each band, and the XUV laser field mainly plays a role on the NSDI probability. Furthermore, an NSDI process can be decoupled into a two-step process: an above-threshold ionization (ATI), followed by a laser-assisted collision (LAC). It is found that, the IR laser field is responsible for broadening the peak in the ATI process and providing additional momenta to the two ionized electrons in the LAC process; while the XUV laser field plays a crucial role on the strength of the spectrum in the ATI process, and influences the radii of orbits in momentum space in the LAC process.

Improved strong-field approximation and quantum-orbit theory: Application to ionization by a bicircular laser field

A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the $T$-matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency $\ensuremath{\omega}$. Special emphasis is on the $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.