Multiphoton Ionization Regime Research Articles

Entanglement in photo-ionization process.

We report a study of the entanglement between the quantized photon field and an atom arising in the photo-ionization process. Our approach is based on an ab initio solution of the time-dependent Schrödinger equation (TDSE) describing the quantum evolution of a bipartite system consisting of the atom and the quantized electromagnetic field. Using the solution of the TDSE, we calculate the reduced photon density matrix, which we subsequently use to compute entanglement entropy. We explain some properties of the entanglement entropy and propose an approximate formula for the entanglement entropy based on the analysis of the density matrix and its eigenvalues. We present the results of a comparative study of the entanglement in the photo-ionization process for various ionization regimes, including the tunneling and the multiphoton ionization regimes.

Role of excitation in the electron rotational asymmetry in circularly polarized laser fields

We comparatively study electron rotational asymmetries in photoionization of excited hydrogen atoms and photodetachment of the fluorine anions in single circularly polarized laser fields by numerically solving the three-dimensional time-dependent Schrödinger equation. We first show that single-photon ionization (or detachment) is more favorable as the electron initially corotates with respect to the direction of the laser field. More interestingly, we systematically demonstrate that the electron rotational asymmetry of the excited hydrogen atom is completely contrary to that of the fluorine anion in the multiphoton ionization (or detachment) regime, which can be attributed to the role played by excited bound states by analyzing the total excitation probability in the excited hydrogen atom. Furthermore, we also confirm that the electron rotational asymmetry of and degenerate orbitals in the excited hydrogen atom changes when the ionization mechanism switches from three-photon to over-the-barrier.

Angular distribution of near-threshold photoelectrons from resonance-enhanced multiphoton ionization of argon

We experimentally study the angular distribution of near-threshold photoelectrons of argon in the multiphoton-ionization regime. Those near-threshold photoelectrons are released from atoms by a weak 800-nm laser field and a strong 400-nm laser field with parallel polarizations. In the laser polarization direction, the yield of the near-threshold photoelectron oscillates with twice the 800-nm laser frequency, while higher-frequency components for the yield oscillations are found for the electrons emitted perpendicular to the laser polarization direction. By decomposing the photoelectron angular distribution into different partial waves, we found that those near-threshold photoelectrons are generated by the interference of different photon channels via resonant states. Moreover, we observed a large time delay between the near-threshold photoelectrons emitted along the laser polarization direction via the $5p$ and $4f$ resonant states.

Evolution of the frequency-comb structure and coherence from a Keldysh multiphoton into a tunneling regime.

We present a theoretical study of the characteristics of the frequency-comb structure and coherence via high-order harmonic generation (HHG) driven by the laser pulse trains when the ionization process is pushed from Keldysh multiphoton into tunneling regime. HHG is obtained by solving accurately the time-dependent Schrödinger equation by means of the time-dependent generalized pseudospectral method. We find that the nested comb structures are formed from each harmonic order in the Keldysh multiphoton ionization regime. But it is severely suppressed or even disappeared in the Keldysh tunneling ionization regime. It implies that the temporal coherence of the emitted frequency comb modes is very sensitive to the Keldysh ionization regime. To understand the evolution of frequency-comb structure and coherence, we perform the calculation of the time-dependent ionization probability and the spectral phase of frequency-comb HHG. We find that the frequency-comb HHG driven by the laser pulse trains in the Keldysh multiphoton regime has a good coherence because the ionization probability of the atom driven by each laser pulse is stable, leading to a phase-coherent frequency-comb structure rather than those cases in the Keldysh tunneling regime with high laser intensity. Our results shed light on current interest and significance to the experimental realization of controllable and frequency-comb vacuum-ultraviolet light sources.

Intense quasi-monochromatic resonant harmonic generation in the multiphoton ionization regime

Resonant high-order harmonics, which result in quasi-monochromatic extreme ultraviolet light with coherent intensity enhancement involving autoionizing resonances, have been demonstrated from laser-ablated plumes in the tunnel-ionization regime. Here, we demonstrate resonant harmonics in the previously unexplored multiphoton-ionization regime. We demonstrate an intense resonant harmonic from gallium with an intensity enhancement ratio of 714 relative to the neighboring harmonics, achieved without the need for extreme ultraviolet filtering methods, thus preventing a typical photon flux loss of more than 70%. Three-dimensional time-dependent Schrödinger equation calculations reveal that this increase in the enhancement ratio is due to the low electron wave packet spreading in the multiphoton-ionization regime. These results reveal a method for increasing the intensity and monochromaticity of intense multimicrojoule femtosecond extreme ultraviolet light and will also facilitate understanding of the involvement of autoionizing resonances in generating resonant harmonics in the multiphoton-ionization regime.

Linear dichroism in few-photon ionization of laser-dressed helium

Ionization of laser-dressed atomic helium is investigated with focus on photoelectron angular distributions stemming from two-color multi-photon excited states. The experiment combines extreme ultraviolet (XUV) with infrared (IR) radiation, while the relative polarization and the temporal delay between the pulses can be varied. By means of an XUV photon energy scan over several electronvolts, we get access to excited states in the dressed atom exhibiting various binding energies, angular momenta, and magnetic quantum numbers. Furthermore, varying the relative polarization is employed as a handle to switch on and off the population of certain states that are only accessible by two-photon excitation. In this way, photoemission can be suppressed for specific XUV photon energies. Additionally, we investigate the dependence of the photoelectron angular distributions on the IR laser intensity. At our higher IR intensities, we start leaving the simple multi-photon ionization regime. The interpretation of the experimental results is supported by numerically solving the time-dependent Schrödinger equation in a single-active-electron approximation.Graphic abstract

Intensity of Resonant Harmonic Generated in the Multiphoton Ionization Regime

The relative intensities of the resonant and nonresonant high-order harmonics, generated by singly charged gallium and indium ions in the field of a laser pulse with a duration of 20 fs and intensity ranging from 5 × 1013 to 2 × 1014 W/cm2, are calculated. The harmonic intensity is found via the matrix element of multiphoton transition within the perturbation theory including the resonant contribution. The latter increases the harmonic intensity at the transition from the ground state to the autoionizing state. We consider laser wavelength when this transition corresponds to 7 and 15 photons.

Mechanism of laser intensity-dependent below-threshold harmonic generation

<sec> High-order-harmonic generation (HHG) is a fundamental atomic and molecular process in strong laser fields and plays a crucial role in the development of ultrafast science and technology. The essential features in HHG, such as the above-threshold harmonic plateau and cutoffs, can be well understood by the semiclassical three-step model. The HHG cutoff occurs approximately at the energy <inline-formula><tex-math id="M1">\begin{document}$3.17{U_{\rm p}} + {I_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M1.png"/></alternatives></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}${I_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M2.png"/></alternatives></inline-formula> is the atomic ionization potential, and <inline-formula><tex-math id="M3">\begin{document}${U_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M3.png"/></alternatives></inline-formula> is the ponderomotive potential.</sec><sec> In the past, most studies focused on the HHG above the ionization threshold, and the general pattern of the HHG spectrum can be qualitatively explained by means of the strong field approximation (SFA) and the quantum treatment of three-dimensional time-dependent Schr?dinger equation (TDSE). However, the SFA results in inadequate description for the process in the harmonic generation below the ionization threshold since it neglects the Coulomb potential and the detailed electronic structure of atoms. Recently, as a promising method to produce vacuum-ultraviolet frequency comb, the HHG in the near- and below-ionization threshold has been increased considerably. However, the dynamical origin of in these lower harmonics is less understood and largely unexplored.</sec><sec> Here we perform an ab initio quantum study of the near- and below-threshold harmonic generation of hydrogen atom by means of the time-dependent generalized pseudospectral method. We study the intensity dependence of the harmonic spectra below the ionization threshold of hydrogen atom in the intense laser field. The high-order harmonic spectra are calculated by the Fourier transform of the atom induced dipole moment in the laser field. The below-threshold harmonic spectra yield is scaled as a function of the laser peak intensity. We find that the spectra yield in below-threshold harmonic generation (BTHG) dependents on the light intensity in the multiphoton ionization regime. And the laser intensity plays an important role in the channel selection process for BTHG. There are mainly two kinds of quantum channels to be responsible for the BTHG. Namely, the generalized short trajectories and the long trajectories, in which the long trajectories are more sensitive to the laser field intensity. Combining with wavelet time-frequency transform, semiclassical trajectories simulation, and quantum channel analysis associated with the laser intensity, the dynamical origin of the BTHG is uncovered.</sec>

Improvement of the ionization factor in the quantitative rescattering theory for simulating macroscopic high-order harmonic generation

We propose to correct the ionization factor in the quantitative rescattering (QRS) theory for a higher precision calculation of macroscopic high harmonic generation (HHG) in a gaseous medium. Compared to the first-order strong-field approximation (SFA-1) and the Ammosov-Delone-Krainov (ADK) ionization models, the Perelomov-Popov-Terent'ev (PPT) model achieves the best agreement with the macroscopic HHG spectra of Ar based on the solution of the time-dependent Schr\odinger equation (TDSE). The investigation of the ionization probability dependence on laser intensity indicates that the PPT model is consistent with the TDSE, both in the tunneling and multiphoton ionization regimes, and the SFA-1 or the ADK mostly works in the tunneling regime. This explains the difference in the total macroscopic harmonic spectra, mainly due to off-axis harmonic emissions generated by small laser intensities. The examples for Ne and Xe by using three ionization models in the QRS theory also show the significance of ionization correction by the PPT model to precisely simulate the macroscopic HHG spectra. This study will help further increase the accuracy of simulating measured HHG spectra quantitatively under a variety of macroscopic conditions.

Probing time delays and coherent imaging of multiphoton resonant ionization

We measure the laser-intensity-dependent photoelectron momentum and energy spectra and identify the emerged resonant $(4s,3d$, and $4f)$ states of multiphoton ionization of Ne at 400 nm. We employ parallelly polarized two-color fields involving a strong ionizing 400-nm field and a weak 800-nm field to probe the relative time delay of resonant states. By analyzing phase-resolved three-dimensional photoelectron momentum distributions, we find the time delay of resonant states has an anisotropic angle dependence. Using an intuitive model, we show that the angle-dependent time delay carries the information of subcycle evolution of quantum states and reflects the temporal coherent properties of multiphoton resonant states during absorption and emission of photons. We find that the relative time delays among the resonant ionization via $4s,3d$, and $4f$ states along the polarization depend on the number of photons absorbed. This study has implications for coherent imaging of electron wave packets in the multiphoton ionization regime.

Symmetry Breaking and Strong Persistent Plasma Currents via Resonant Destabilization of Atoms.

The ionization rate of an atom in a strong optical field can be resonantly enhanced by the presence of long-living atomic levels (so-called Freeman resonances). This process is most prominent in the multiphoton ionization regime, meaning that the ionization event takes many optical cycles. Nevertheless, here, we show that these resonances can lead to rapid subcycle-scale plasma buildup at the resonant values of the intensity in the pump pulse. The fast buildup can break the cycle-to-cycle symmetry of the ionization process, resulting in the generation of persistent macroscopic plasma currents which remain after the end of the pulse. This, in turn, gives rise to a broadband radiation of unusual spectral structure, forming a comb from terahertz to visible. This radiation contains fingerprints of the attosecond electron dynamics in Rydberg states during ionization.

Effect of two-center interference on molecular ionization in multiphoton ionization regime.

Using solution of the full three-dimensional time-dependent Schrödinger equation (TDSE) in prolate spheroidal coordinates, we investigate the orientation dependence of ionization of H2+ in near-infrared laser fields. It is found that, the ionization probability decreases as a function of the alignment angle in tunneling ionization regime, while it ascends with the increase of orientation angle in multiphoton ionization regime for the internuclear distance R=2 a.u. Furthermore, the result obtained by the length gauge strong-field approximation theory is in qualitative agreement with that calculated by the TDSE but the radiation gauge strong-field approximation and molecular ADK theories fail to reproduce the TDSE result. Analysis indicates that the above intriguing feature can be ascribed to the interference between the partial electron wave packets emitted from different molecular cores, which becomes evident at low laser intensity due to increased width of the initial mechanical momentum of the photoelectron at ionization moment. In addition, when the internuclear distance increases to R=4 a.u., the ionization yields decrease vs alignment angle in both tunneling and multiphoton regimes since the electron wavefunction of the 1σg orbit is more concentrated in the molecular axis than that of R=2 a.u.

The possibility for calibrating laser intensity in strong-field-ionization experiments

SynopsisWe present a simple method, based on an improved Perelomov-Popov-Terent’ev (PPT) model, for calibrating laser intensities from the measured ionization probabilities (or signals) of atoms or molecules in an intense laser fields. We emphasize that the PPT model can work very well both in the multiphoton and tunneling ionization regimes.

Effects of ultrashort laser pulses on angular distributions of photoionization spectra

We study the photoelectron spectra by intense laser pulses with arbitrary time dependence and phase within the Keldysh framework. An efficient semianalytical approach using analytical transition matrix elements for hydrogenic atoms in any initial state enables efficient and accurate computation of the photoionization probability at any observation point without saddle point approximation, providing comprehensive three dimensional photoelectron angular distribution for linear and elliptical polarizations, that reveal the intricate features and provide insights on the photoionization characteristics such as angular dispersions, shift and splitting of photoelectron peaks from the tunneling or above threshold ionization(ATI) regime to non-adiabatic(intermediate) and multiphoton ionization(MPI) regimes. This facilitates the study of the effects of various laser pulse parameters on the photoelectron spectra and their angular distributions. The photoelectron peaks occur at multiples of 2ħω for linear polarization while odd-ordered peaks are suppressed in the direction perpendicular to the electric field. Short pulses create splitting and angular dispersion where the peaks are strongly correlated to the angles. For MPI and elliptical polarization with shorter pulses the peaks split into doublets and the first peak vanishes. The carrier envelope phase(CEP) significantly affects the ATI spectra while the Stark effect shifts the spectra of intermediate regime to higher energies due to interference.

Quantum-Mechanical Description of Ionization-Induced Generation of Tunable Mid-Infrared Pulses

The work is devoted to the analytical study of the excitation of low-frequency current density (with frequencies much smaller than the frequency of the optical wave) which radiates in mid-infrared band in the gas ionization by two-color laser pulses. We calculate the low-frequency current density using the analytical solution of time-dependent Schrödinger equation on the basis of strong-field approximation. Closed-form analytical formulas for the low-frequency current density are obtained for laser-pulse parameters corresponding the tunneling and multiphoton ionization regimes. The features of excitation of low-frequency current density are analyzed in both regimes.

Terahertz and higher-order Brunel harmonics: from tunnel to multiphoton ionization regime in tailored fields

Brunel radiation appears as a result of a two-step process of photo-ionization and subsequent acceleration of electron, without the need of electron recollision. We show that for generation of Brunel harmonics at all frequencies, the subcycle ionization dynamics is of critical importance. Namely, such harmonics disappear at the low pump intensities when the ionization dynamics depends only on the slow envelope (so-called multiphoton ionization regime) and not on the instantaneous field. Nevertheless, if the pump pulse contains incommensurate frequencies, Brunel mechanism does generate new frequencies even in the multiphoton ionization regime.

Exploration of laser-driven electron-multirescattering dynamics in high-order harmonic generation.

Multiple rescattering processes play an important role in high-order harmonic generation (HHG) in an intense laser field. However, the underlying multi-rescattering dynamics are still largely unexplored. Here we investigate the dynamical origin of multiple rescattering processes in HHG associated with the odd and even number of returning times of the electron to the parent ion. We perform fully ab initio quantum calculations and extend the empirical mode decomposition method to extract the individual multiple scattering contributions in HHG. We find that the tunneling ionization regime is responsible for the odd number times of rescattering and the corresponding short trajectories are dominant. On the other hand, the multiphoton ionization regime is responsible for the even number times of rescattering and the corresponding long trajectories are dominant. Moreover, we discover that the multiphoton- and tunneling-ionization regimes in multiple rescattering processes occur alternatively. Our results uncover the dynamical origin of multiple rescattering processes in HHG for the first time. It also provides new insight regarding the control of the multiple rescattering processes for the optimal generation of ultrabroad band supercontinuum spectra and the production of single ultrashort attosecond laser pulse.

Helicity sensitive enhancement of strong-field ionization in circularly polarized laser fields.

We investigate the strong-field ionization from p± orbitals driven by circularly polarized laser fields by solving the two-dimensional time-dependent Schrödinger equation in polar coordinates with the Lagrange mesh technique. Enhancement of ionization is found in the deep multiphoton ionization regime when the helicity of the laser field is opposite to that of the p electron, while this enhancement is suppressed when the helicities are the same. It is found that the enhancement of ionization is attributed to the multiphoton resonant excitation. The helicity sensitivity of the resonant enhancement is related to the different excitation-ionization channels in left and right circularly polarized laser fields.

Exploring laser-driven quantum phenomena from a time-frequency analysis perspective: a comprehensive study.

Time-frequency (TF) analysis is a powerful tool for exploring ultrafast dynamics in atoms and molecules. While some TF methods have demonstrated their usefulness and potential in several quantum systems, a systematic comparison among them is still lacking. To this end, we compare a series of classical and contemporary TF methods by taking hydrogen atom in a strong laser field as a benchmark. In addition, several TF methods such as Cohen class distribution other than the Wigner-Ville distribution, reassignment methods, and the empirical mode decomposition method are first introduced to exploration of ultrafast dynamics. Among these TF methods, the synchrosqueezing transform successfully illustrates the physical mechanisms in the multiphoton ionization regime and in the tunneling ionization regime. Furthermore, an empirical procedure to analyze an unknown complicated quantum system is provided, suggesting the versatility of TF analysis as a new viable venue for exploring quantum dynamics.

Excited state dynamics in SO2. III. An ab initio quantum study of single- and multi-photon ionization

We present an ab initio quantum study of the photoelectron spectra of sulfur dioxide, based on wavepacket propagations on manifolds of ionic, and excited/Rydberg states. We obtain excellent agreement for two different cases. First, the one photon ionization case where we can reproduce all details of the experimental spectrum and demonstrate the influence of the conical intersection between two of the ionic states. Then the multiphoton ionization regime, in which the dynamics of the wave packet on the two lowest singlet states is directly mapped in the spectra via a pump-probe scheme, as proposed in the experimental companion paper [I. Wilkinson et al., J. Chem. Phys. 140, 204301 (2014)].