Above-threshold Ionization Peaks Research Articles

Energy and angular distributions of electrons from sodium atoms photo-ionized with femtosecond laser pulses

We studied photoelectron angular distributions (PADs) and energy spectra of sodium atoms photo-ionized with intense short laser pulses in the near-infrared region. Energy spectra of photoelectrons due to multistep ionization of sodium atoms through intermediate levels 5p, 6p, 7p, and 4f were observed in above threshold ionization (ATI) at laser intensities of 2 × 1013 W cm−2 and 1 × 1013 W cm−2. The PADs from the 5p(4f) state for zero, first, second and third order ATI peaks were measured. We observed that for the two selected laser intensities the angular distribution of photoelectrons showed only slight variations. The PADs exhibit main lobes within ∼60° degrees from the laser polarization and additional lobes that become more pronounced with the increasing ATI peak number. Besides a general analytical representation of the observed angular dependences, the experimental PADs for each ATI peak were fitted with Legendre polynomials accounting for different ionization channels. The good agreement between the experimental data and fitting functions allowed to evaluate the contributions of the ionization channels to the observed ATI orders. The calculations of the photoelectron spectra by numerically solving the time-dependent Schrödinger equation in a single active electron approximation produced agreement with the experiment in the main features of the spectra, while differences in more subtle details were observed.

Semiclassical analysis of photoelectron interference in a synthesized two-color laser pulse

We measure the photoelectron energy spectra from strong-field ionization of Kr in a two-color laser pulse consisting of a strong 400-nm field and a weak 800-nm field. The intensities of the main above-threshold ionization (ATI) and sideband peaks in the photoelectron energy spectra oscillate roughly oppositely with respect to the relative phase between the two-color components. We study the photoelectron interferometry in strong-field ATI regime from the view of interference of different electron trajectories in order to extend RABBITT type analysis to the strong-field regime. Based on the strong-field approximation model, we obtain analytical expressions for the oscillations of both ATI and sideband peaks with the relative phase. A phase shift of \pi/4 with respect to the field maximum of the two-color laser pulse is revealed for the interference maximum in the main ATI peak without including the effect of the atomic potential.

Study of the circular dichroism of He+ ion

We study the mechanism of circular dichroism (CD) in $ {{\rm He}^ + } $He+ under XUV and NIR pulses in the experimental condition presented by Ilchen et al. [Phys. Rev. Lett.118, 013002 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.013002] and in a range of pulse intensities and durations by solving the time-dependent Schrodinger equation (TDSE) in momentum space. The method enables investigation of the ionization and intermediate transition probabilities of $ {{\rm He}^ + } $He+ in detail. We show that the lowest-order perturbation theory (LOPT) is qualitatively sufficient to describe experimental results and find that ionization favors co- and counter-rotating pulses for NIR intensities in and beyond LOPT regimes, respectively. In the experimental pulse duration, we show that a sub-peak along the first above-threshold ionization peak exists in the counter-rotating case due to one-photon absorption from excited states, which cannot be obtained by solving TDSE with a short duration of 22 fs, since the energy band width is too wide to resolve this substructure. We present the variation of CD values with NIR intensities.

Nonresonant multiphoton ionization of xenon atoms by femtosecond laser pulses

We experimentally study multiphoton ionization of xenon atoms by 266 nm, 400 nm and 800 nm femtosecond laser pulses. The measurements of photoelectron kinetic energy and photoelectron angular distribution indicate that nonresonant multiphoton ionization occurs in the present experimental condition. It obeys the dipolar selection rule and the angular momentum changes one quantum number for adjacent above-threshold ionization peaks.

Universal Description of the Attoclock with Two-Color Corotating Circular Fields.

We experimentally measure the laser-intensity-dependent photoelectron momentum distributions (PMDs) of Ar atoms with two-color (ω+2ω) corotating circularly polarized fields. The interference patterns on PMDs reveal complex structures with respect to the laser intensity ratio. The main above-threshold ionization peaks and sidebands on PMD distribute oppositely when the fundamental field is much weaker than the second-harmonic field, and the PMD reveals a characteristic single-lobe distribution when the two colors have comparable intensities. Using strong-field approximation, we analytically explain how the interference pattern on PMD evolves with respect to the relative laser intensity. By analyzing the interference pattern, we reveal the phase difference and the temporal evolution of the emitting electron wave packets. We show that, when monitoring the intensity ratio, the double-pointer attoclock geometry with corotating circular fields can be universally mimicked as the spatially rotating temporal double-slit experiments with the variable slit width, which can be used to probe and control strong-field ionization.

Chirp and carrier-envelope-phase effects in the multiphoton regime: measurements and analytical modeling of strong-field ionization of sodium

We investigate the influence of chirp on carrier-envelope-phase (CEP)-dependent strong-field few-cycle laser-induced photoelectron spectra of sodium, well within the multiphoton regime. Our measurements and analytical model of this process reveal a simple chirp-dependence, which has the potential to be utilized as an online monitor of laser chirp. Moreover, this effect could extend single-shot measurements of the CEP using above-threshold ionization to longer, chirped pulses, and significantly lower the required pulse energies. Specifically, at a wavelength of 775 nm and an intensity of the CEP- and energy-dependent left-right asymmetries of emitted electrons are measured in a time-of-flight spectrometer. In these asymmetry maps, inclined stripe-like structures emerge, where the inclination is tunable with the chirp of the pulse. We report a simple analytical model, explaining the effect as the interference of electrons with even and odd angular momenta, located at energies in between adjacent above-threshold ionization peaks. As we demonstrate, the analytical model is in good agreement with the measurement, as well as with solutions of the three-dimensional time-dependent Schrödinger equation. Further, the analytical model, which can easily be extended to other atoms, allows us to derive an equation, describing the relation between the slope of the inclined stripes and the chirp of the laser.

Ionization of hydrogen atom by n-cycle circularly polarized laser pulses

The energy-dependent phenomena of the photoelectron angular distributions (PADs) for different above-threshold ionization (ATI) peaks are investigated by means of the ionization of H atom in few-pulse laser fields with different optical cycle numbers. We find that for one-cycle laser pulse, the PADs and the photoelectron energy spectra are inversion asymmetric , and the emitting direction is not dependent on the photoelectric energy, but only on the carrier-envelope (CE) phase of the laser pulse. For three-cycle laser pulse, although the photoelectron energy spectra are still inversion asymmetric , the emitting direction is dependent on the photoelectric energy, besides the CE phase. This energy-dependent phenomena becomes more obvious for six-cycle laser pulse. When the number of the optical cycle is twelve, however, the photoelectron energy spectra are almost inversion symmetric especially for the low-order ATI peaks, and the bright rings in the momentum distributions are nearly perfect and isotropic. The phenomena show that if the number of cycles of the laser pulse are larger, the ionization behaviors of atom will extend to that of atom in an infinitely monochromatic plane wave.

Above-threshold ionization of diatomic molecules in an intense laser field: Molecular alignment effects

In this work, we study the photoelectron spectra of the diatomic molecule O2 in the direction perpendicular to the laser polarization. Compared with atoms, molecules have additional parameters, e. g., the orientation of the molecule and the symmetry of the initial electronic state, and thus give rise to richer strong-field phenomena. Our simulations show that for parallel and perpendicular alignments of the laser polarization with respect to the molecular axis, the photoelectron spectra display above-threshold ionization (ATI) peaks with a specific 2 (h) over bar omega. separation in which the absorption of an even number of photons is absent. However, for other alignment angles, the even-order ATI peaks appear. According to our analysis, the physical mechanism of the alignment effect of the even-order ATI peaks can be attributed to the symmetry of the molecular ground-state wave function with respect to the photoelectron emission direction.

Investigation of interference effect during ionization of hydrogen atom in bichromatic laser fields of circular polarization

We theoretically investigate the strong-field ionization of hydrogen atom in bichromatic laser fields of circular polarization by calculating the momentum distributions. We find that the momentum distributions consist of a series of arc fringes, which correspond to the different above-threshold ionization peaks, and the momentum distributions generally are inversion asymmetric owing to the interference happening between the different ionization channels. But if only one ionization channel is considered, the momentum distributions are perfect and concentric rings, and as the number of ionization channel increases, the asymmetry of the momentum distribution becomes more and more notable.

Macro-atom versus many-electron effects in ultrafast ionization of C60

Ionization mechanisms of C${}_{60}$ molecules irradiated by a short intense 800-nm laser pulse are studied. Angle-resolved photoelectron spectra show above-threshold ionization (ATI) patterns with a low peak contrast and a remarkably smooth angular distribution. The results are interpreted by combining two theoretical models. A time-dependent Schr\odinger equation (TDSE) calculation based on the $B$-spline method that explicitly takes into account the molecular potential mimics the single-active-electron response while a statistical model accounts for the many-electron effects. We show that the latter are responsible for the loss of contrast in the ATI peaks. The smooth angular distribution arises in the TDSE calculation as a result of the high angular momentum of the C${}_{60}$ ground electronic state and therefore is a manifestation of the atomic behavior of the molecule.

Secondary peaks in the atomic ionization by a resonant laser pulse

The above-threshold ionization of atoms by XUV short laser pulses with frequencies resonant with a ground-excited state transition is investigated. A theory based on a variational expression with trial wave functions for the final and the initial states is presented. For the former we use a Coulomb-Volkov wave function, and for the latter a close-coupling solution of the time-dependent Schrödinger equation considering a few bound states and their depletion towards the continuum. We find that this discrete-continuum Coulomb-Volkov theory provides a very good description of the photoelectron spectrum. In particular it accounts for the splitting of the above-threshold ionization peaks by Rabi oscillations and the appearance of secondary-peaks observed in full numerical simulations.

Position–momentum correlations in electron–ion scattering in strong laser fields

The quantum Wigner function of an electron scattered by an ion in a strong laser field is considered in the framework of a one-dimensional scattering model with a soft-core Coulomb potential. The Wigner function contains much more information on the scattering process than the projected probability distributions in position and momentum space considered previously. The formation of the above-threshold ionization (ATI) energy spectrum, including ATI peaks, modulations and transients, can be easily explained by using the interference of phase-space trajectories.

Computational Investigation of the Interaction Between Hydrogen Atoms and an Intense Circularly Polarized Laser Field

AbstractThe study of interactions between a high-power laser and atoms has been one of the fundamental and interesting topics in strong field physics for decades. Based on a nonperturbative model, ten years ago, we developed a set of programs to facilitate the study of interactions between a circularly polarized laser and atomic hydrogen. These programs included only contribution from the bound states of the hydrogen atom. However, as the laser intensity increases, contribution from continuum states to the excitation and ionization processes becomes larger and can no longer be neglected. Furthermore, because the original code is not able to add this contribution directly due to its many disadvantages, a major upgrade of the code is required before including the contribution from continuum states in future. In this paper, first we deduce some important formulas for contribution of continuum states and present modifications and tests for the upgraded code in detail. Second we show some comparisons among new results, old results from the original codes and the available experimental data. Overall the new result agrees with experimental data well. Last we present our calculation of above-threshold ionization (ATI) rate and compare it with a pertuba-tive calculation. The comparison shows that our nonperturbative calculation can also produce ATI peak suppression.

Floquet analysis of real-time wave functions without solving the Floquet equation

We propose a method to obtain Floquet states---also known as light-induced states---and their quasi-energies from real-time wavefunctions without solving the Floquet equation. This is useful for the analysis of various phenomena in time-dependent quantum dynamics if the Hamiltonian is not strictly periodic, as in short laser pulses, for instance. There, the population of the Floquet states depends on the pulse form and is automatically contained in the real-time wavefunction but not in the standard Floquet approach. Several examples in the area of intense laser-atom interaction are exemplarily discussed: (i) the observation of even harmonics for an inversion-symmetric potential with a single bound state; (ii) the dependence of the population of Floquet states on (gauge) transformations and the emergence of an invariant, observable photoelectron spectrum; (iii) the driving of resonant transitions between dressed states, i.e., the dressing of dressed states, and (iv) spectral enhancements at channel closings due to the ponderomotive shift of above-threshold ionization peaks.

Study of the ionization of hydrogen atoms in an intense circularly polarized laser field

Based on the non-relativistic theory and dipole approximation, we have developed a new program to study the interaction between a circularly polarized laser and hydrogen atoms. In this paper, we present our calculation of above-threshold ionization (ATI) rate based on the new code and compare the results with that of a pertubation theory calculation. The comparison shows that our non-perturbative calculations can produce ATI peak suppression.

Interference substructure of above-threshold ionization peaks in the stabilization regime

The photoelectron spectra produced in the photodetachment of ${\mathrm{H}}^{\ensuremath{-}}$ (treated in the single-active-electron approximation) by strong high-frequency laser pulses with adequately chosen laser parameters in the stabilization regime are theoretically studied for elliptic polarization over an extended parameter range. An oscillating substructure in the above-threshold ionization peaks is observed, which confirms similar findings in the one-dimensional (1D) [K. Toyota et al., Phys. Rev. A 76, 043418 (2007)] and 3D calculations for linear polarization [O. I. Tolstikhin, Phys. Rev. A 77, 032712 (2008)]. The mechanism is an interference between the photoelectron wave packets created in the rising and falling parts of the pulse which is specific to the stabilization regime. We thus conclude that this interference substructure is robust for any polarization and over a wide range of the laser parameters, and hence should be observable experimentally.

Finite-bandwidth effects in strong-field ionization of atoms by few-cycle circularly polarized laser pulses

In the strong-field approximation, we calculate the electron momentum distribution following strong-field ionization of atomic hydrogen by an $N$-cycle circularly polarized laser pulse. For $N\ensuremath{\lesssim}5$, our results show a pronounced interference structure in addition to the well-known carrier-envelope phase difference (CEPD) sensitivity. With increasing $N$ we observe a gradual change to a momentum distribution which is free of interference and CEPD effects and which is characterized by well-resolved above-threshold ionization peaks, consistent with the quantized photon picture. The changes in the interference structures are explained by the spectral properties of the pulse. We compare the results of the strong-field approximation with those obtained by the saddle-point method and show that while the saddle-point method is able to reproduce the results for $N\ensuremath{\gtrsim}5$, it fails to explain the interference structure and the asymmetry of the distribution for smaller $N$.

Above-threshold ionization of Mg by linearly and circularly polarized laser fields: Origin of the subpeaks in the photoelectron energy spectra

We theoretically investigate above-threshold ionization of Mg by linearly and circularly polarized fs laser pulses. We find that the above-threshold ionization peaks are accompanied by small subpeaks for both linearly and circularly polarized pulses. We interpret the physical origin of the subpeaks as above-threshold ionization from the low-lying bound states which are far off-resonantly excited by the spectral wing of the pulse. This interpretation is confirmed by our comparative numerical studies. Furthermore, we provide a clear explanation of why this kind of subpeak in the photoelectron energy spectra has not been reported for smaller photon energies with Mg and other commonly used atoms such as H and rare gas atoms.

Ionization by short uv laser pulses: Secondary above-threshold-ionization peaks of the electron spectrum investigated through a modified Coulomb-Volkov approach

The interaction between an atom and a short laser pulse is studied in the case where both photon energies are smaller than the ionization potential and perturbation conditions prevail. Under these conditions, a full numerical solution of the time-dependent Schr\odinger equation for a hydrogen atom initially in its ground state shows that secondary peaks show up in the above-threshold ionization (ATI) spectrum. We introduce here an easy-to-implement approximation that sheds light on these features. This approach, which is based on Coulomb-Volkov-type states, is an extension of a previous theory that applies only when photon energies are greater than the ionization potential. We show that introducing a coupling to intermediate bound states into the approach permits to nicely reproduce the full numerical electron spectrum for smaller photon energies. Further, it allows us to trace back unambiguously the secondary peaks to a manifold process, i.e., excitation of transient bound states followed by multiphoton absorption, and to show that the main ATI peaks may be enhanced by intermediate state contributions. When bound states with $1\ensuremath{\leqslant}n\ensuremath{\leqslant}4$ are included, the approach provides excellent predictions for photon energies as low as half the ionization potential.

Gradual broadening of successive above-threshold-ionization peaks

We present theoretical calculations that show a systematic increase of the spectral widths of the successive above-threshold-ionization (ATI) peaks using Fourier-limited pulses. The increase of the width is attributed to the effective Fourier width corresponding to the higher-order processes. Based on that interpretation, we propose a simple model of calculating the width of a $N\mathrm{th}$-order ATI peak. We compare the results obtained from this model to the results obtained through the direct propagation of the time-dependent Schr\odinger equation. For this, we have selected the negative hydrogen ion that represents the simplest possible system to study this feature due to the absence of resonances, that may obscure the results. Considering that Fourier-limited laser pulses with duration of the order of few tens of fs and wavelengths around the optical regime are nowadays readily available, we address the question about the nature of the photoelectron energy spectrum when the atoms are exposed in such fields.