arXiv subjects

Mohsen Vafaee

Publications and source records attributed to Mohsen Vafaee.

13 recordsLinked to original sources

arXiv2019

Static coherent states method for investigating high-order harmonic generation in single-electron molecular systems

In this report, a novel methodology based on the static coherent states approach is introduced with the capability of calculating various strong-field laser-induced nonlinearities in full dimensional single-electron molecular systems; an emphasis is made on the high-order harmonic generation. To evaluate the functionality of this approach, we present a case study of the Hydrogen molecular ion \ih interacting with a few-cycle linearly polarized optical laser with trapezoidal waveform. We detected that the accuracy of the obtained harmonics is considerably enhanced by averaging the expectation value of the acceleration of the single electron over a set of identical random simulations. Subsequently, the presented approach demands a significantly lower number of basis sets than the regular exact three dimensional unitary split-operator solvers of time dependent Schr{ö}dinger equation that necessitate an extremely large number of data points in the coordinate space, and so the computational cost. Additionally, applying static coherent states method, we have investigated isolated attosecond pulse generation using the polarization gating technique, which combines two delayed counter rotating circular laser pulses, and opens up a gate at the central portion of the superposed pulse.

quant-ph↗

arXiv2018

Nonadiabatic electron dynamics effects on high-harmonic generation spectrum of H$_2^+$: minima and oscillatory pattern

We numerically solved the full-dimensional electronic time-dependent Schrödinger equation for H$_2^+$ with Born-Oppenheimer approximation under different sin$^2$-shaped and trapezoidal laser pulses at some different wavelengths, with $I=$1 $\times 10^{13}$ Wcm$^{-2}$, 3 $\times 10^{13}$ Wcm$^{-2}$, and 6 $\times 10^{13}$ Wcm$^{-2}$ intensity at 4.73 a.u. and 7.0 a.u. internuclear distances. Some structures such as complexity, minima, and oscillatory patterns appeared in the high-order harmonic generation (HHG) spectra are investigated in this work by considering the electron localization, electron nonadiabatic dynamics, spatially asymmetric of the HHG, and the Rabi frequency of the population of the ground and excited electronic states to better understand the origins of these structures in the HHG spectrum. We will clear that the origin of complicated patterns of the HHG spectra in sin$^2$-shaped laser pulse is due to that the most portion of the HHG emission occurs at the falling part of the laser pulse. We explore that the oscillatory pattern in the HHG spectra originate from an oscillatory pattern in the $S_g$ and $S_u$ spectra and these oscillatory patterns in turn are due to the nonadiabatic electronic behavior appeared as the slow oscillation pattern in the ground and first excited electronic states populations. Also, our result shows that the minima of the HHG are related to the oscillatory patterns in $S_g$ and $S_u$ spectra.

physics.atom-ph↗

arXiv2018

Four-Photon Kapitza-Dirac Effect as Electron Spin Filter

We theoretically demonstrate the feasibility of producing electron beam splitter using Kapitza-Dirac diffraction on bichromatic standing waves which are created by the fundamental frequency and the third harmonic. The relativistic electron in Bragg regime absorbs three photons with frequency of w and emits a photon with frequency of 3w, four-photon Kapitza-Dirac effect. In this four-photon Kapitza-Dirac effect distinct spin effects arise in different polarizations of the third harmonic laser beam. It is shown that the shape of Rabi oscillation between initial and scattered states is changed and finds two unequal peaks. In circular polarization for fundamental and third harmonic, despite Rabi oscillation, the spin down electron in 0.56 fs intervals maintains its momentum and spin. Also we present an electron spin filter with combination of a linearly polarized fundamental laser beam and a third harmonic with circular polarization that scatters the electron beam according to its spin state.

physics.atom-ph↗

arXiv2017

Contribution of the pre-ionized H$_2$ and the ionized H$_2^+$ subsystems to the HHG Spectra of H$_2$ in intense laser fields

Contributions of the pre-ionized H$_2$ (PI-H$_2$) and ionized H$_2^+$ subsystems of the two-electron H$_2$ system to its high-order harmonic generation in 8-cycle $\sin^{2}$-like ultrafast intense laser pulses are calculated and analyzed based on the solution of the time-dependent Schrödinger equation (TDSE) for the one-dimensional two-electronic H$_2$ system with fixed nuclei. The laser pulses have $λ =\ 390\ \&\ 532$ nm wavelengths and $I=1\times 10^{14}$, 5$\times 10^{14}$, 1$\times 10^{15}$ \&\ 5$\times 10^{15}$ Wcm$^{-2}$ intensities. It is found that at the two lower intensities, the PI-H$_2$ subsystem dominantly produces the HHG spectra. While, at the two higher intensities, both PI-H$_2$ and ionized H$_2^+$ subsystems contribute comparably to the HHG spectra. In the H$_2^+$ subsystem, the symmetry of the populations of H$_2^+$(I) and H$_2^+$(II) regions (left and right regions of H$_2^+$ subsystem) is broken by increasing the laser intensity. Complex patterns and even harmonics also appear at these two higher intensities. For instance, at $1\times 10^{15}$ Wcm$^{-2}$ intensity and $λ$ = 532 nm, the even harmonics are appeared near cut-off region. Interestingly, at $5\times 10^{15}$ Wcm$^{-2}$ intensity and $λ$ = 390 nm, the even harmonics replaced by the odd harmonics with red shift. At $λ$ = 390 \&\ 532 nm and $I=1\times 10^{15}$ intensity, the two-electron cutoffs corresponding to nonsequential double-recombination (NSDR) with maximum return kinetic energy of 4.70$U_p$ are detected. The HHG spectra of the whole H$_2$ system obtained with and without nuclear dynamics treated classically are approximately similar. However, at $1\times 10^{15}$ Wcm$^{-2}$ intensity and $λ$ = 532 nm, if we take into account nuclear dynamics, the even harmonics which are appeared near cutoff region, replaced by the odd harmonics with blue shift.

physics.atom-ph↗

arXiv2016

A new version of fermion coupled coherent states method: Theory and applications in simulation of two-electron systems

We report a new version of fermion coupled coherent states method (FCCS-II) to simulate two-electron systems based on a self-symmetrized six-dimensional (6D) coherent states grid. Unlike the older fermion coupled coherent states method (FCCS-I), FCCS-II does not need any new equations in comparison with the coupled coherent states method. FCCS-II uses a simpler and more efficient approach for symmetrizing the spatial wave function in the simulation of fermionic systems. This method, has significantly increased the speed of computations and give us the capability to simulate the quantum systems with the larger CS grids. We apply FCCS-II to simulate the Helium atom and the Hydrogen molecule based on grids with a large numbers of coherent states. FCCS-II with a relatively low number of CS gives a potential energy curve for H2 that is very close to the exact potential curve. Moreover, we have re-derived all the important equations of the FCCS-I method.

physics.atom-ph↗

arXiv2014

Effect of nuclear motion on high-order harmonic generation of H$_2^+$ in intense ultrashort laser pulses

High-order harmonic generation is investigated for H$_2^+$ and D$_2^+$ with and without Born-Oppenheimer approximation by numerical solution of full dimensional electronic time-dependent Schrödinger equation under 4-cycle intense laser pulses of 800 nm wavelength and $I$=4, 5, 7, 10 $\times 10^{14}$ W$/$cm$^2$ intensities. For most harmonic orders, the intensity obtained for D$_2^+$ is higher than that for H$_2^+$, and the yield difference increases as the harmonic order increases. Only at some low harmonic orders, H$_2^+$ generates more intense harmonics compared to D$_2^+$. The results show that nuclear motion, ionization probability and system dimensionality must be simultaneously taken into account to properly explain the isotopic effects on high-order harmonic generation and to justify experimental observations.

physics.atom-ph↗

arXiv2013

High harmonic generation from pre-ionized H$_2$ in ultrashort intense laser fields

Effects of the laser pulse wavelength and intensity on the HHG production from the \textit{ionic} and \textit{homolytic} pre-ionization transient states of the two-electron H$_{2}$ system exposed to ultrashort intense laser pulses are studied by solving time-dependent Schrödinger equation. It is found that for the populated homolytic species in each half cycle of the laser pulse having enough strength, a pair of strong and weak HHG radiations are produced simultaneously. For the populated ionic species divided into two regions, in each half cycle, one of the ionic regions has a strong radiation and the other ionic region has a weak HHG radiation. The HHG spectra of the homolytic and ionic species are almost similar, except that in some limited parts of the HHG spectrum, one of them dominate the other.

physics.atom-ph↗

arXiv2012

Precise Calculation of Single and Double Ionization of Hydrogen Molecule in Intense Laser Pulses

A new simulation box setup is introduced for the precise description of the wavepacket evolution of two electronic systems in intense laser pulses. In this box, the regions of the hydrogen molecule H$_{2} $, and singly and doubly ionized species, H$_{2}^+ $ and H$_{2}^{+2} $, are well recognized and their time-dependent populations are calculated at different laser field intensities. In addition, some new regions are introduced and characterized as quasi-double ionization and their time-dependencies on the laser field intensity are calculated and analyzed. The adopted simulation box setup is special in that it assures proper evaluation of the second ionization. In this study, the dynamics of the electrons and nuclei of the hydrogen molecule are separated based on the adiabatic approximation. The time-dependent Schrödinger and Newton equations are solved simultaneously for the electrons and the nuclei, respectively. Laser pulses of 390 nm wavelength at four different intensities (i.e. $ 1\times10^{14} $, $ 5\times10^{14} $, $ 1\times10^{15} $, and $ 5\times10^{15} $ W cm$^{-2}$) are used in these simulations. Details of the central H$_{2} $ region is also presented and discussed. This region is divided into four sub-regions related to the ionic state H$^+$H$^-$ and covalent (natural) state HH. The effect of the motion of nuclei on the enhanced ionization is discussed. Finally, some different time-dependent properties are calculated and their dependencies on the intensity of the laser pulse are studied, and their correlations with the populations of different regions are analyzed.

physics.atom-ph↗

arXiv2011

Nuclear classical dynamics of H$_2$ in intense laser field

In the first part of this paper, the different distinguishable pathways and regions of the single and sequential double ionization are determined and discussed. It is shown that there are two distinguishable pathways for the single ionization and four distinct pathways for the sequential double ionization. It is also shown that there are two and three different regions of space which are related to the single and double ionization respectively. In the second part of the paper, the time dependent Schrödinger and Newton equations are solved simultaneously for the electrons and the nuclei of H$_2$ respectively. The electrons and nuclei dynamics are separated on the base of the adiabatic approximation. The soft-core potential is used to model the electrostatic interaction between the electrons and the nuclei. A variety of wavelengths (390 nm, 532 nm and 780 nm) and intensities ($5\times10^{14}$ $Wcm^{-2} $ and $ 5\times10^{15}$ $Wcm^{-2}$) of the ultrashort intense laser pulses with a sinus second order envelope function are used. The behaviour of the time dependent classical nuclear dynamics in the absence and present of the laser field are investigated and compared. In the absence of the laser field, there are three distinct sections for the nuclear dynamics on the electronic ground state energy curve. The bond hardening phenomenon does not appear in this classical nuclear dynamics simulation.

physics.atom-ph↗

arXiv2010

Pathway of D$^{+}$ in Sequential Double Ionization of D$_2$ in an Intense Laser Pulse

We show the details of the pathway for dissociative ionization process of ground electronic state of aligned D$^{+}_{2}$ due to first ionization of D$_2$ in short ($\thicksim$100 fs) and intense ($4.0\times10^{14}$ W cm$^{-2}$) 480 nm laser pulses. The initial vibrational state of D$^{+}_{2}$ comes from the vertical transformation of the ground state of D$_{2}$. The initial wavepacket in the ground electronic state of D$_{2}^{+}$ is outgoing through dissociation-ionization channel accompanied by a strong coupling between $1s σ_{g}$ and $2p σ_{u}$ electronic states. We show explicitly that the transition from the coupling states $1s σ_{g}$ and $2p σ_{u}$ to the ionization state is not a direct transition but takes place through other intermediate states with some dissociation energy that results in the internuclear distribution of the ionization to move considerably to larger internuclear distances.

physics.atom-ph↗

arXiv2008

Nuclear kinetic energy spectra of D_2^+ in intense laser field: Beyond Born Oppenheimer approximation

Simultaneously, the vibrational nuclear dynamics and full dimensional electronic dynamics of the deuterium molecular ion exposed to the linear polarized intense laser field are studied. The time dependent Schrödinger equation of the aligned D2+ with the electric laser field is solved for the simulation of the complicated dissociative ionization processes and compared with the recent related experimental results. In this work, the R-dependent ionization rate and the enhanced ionization phenomenon beyond the Born-Oppenheimer approximation (BOA) are introduced and calculated. The substructure of the nuclear kinetic energy release spectra are revealed as the Coulomb explosion energy spectra and dissociation energy spectra in the dissociation-ionization channel. The significant and trace of these distinct sub-spectra in the total spectra comparatively are displayed and discussed.

physics.atom-ph↗

arXiv2006

Detailed instantaneous ionization rate of H$_2^+$ in intense laser field

Component instantaneous ionization rate (IIR) is introduced and the approach of its calculation is formulated. The component IIR's and the overall (time-averaged) component ionization rates are calculated for H$_2^+$ at different values of inter-nuclear distance in a linearly polarized laser field with $1.0 \times10^{14}$W cm$^{-2}$ intensity and $λ\sim 1064 $nm wavelength by direct numerical solution of the fixed-nuclei full dimensional time-dependent Schr ödinger equation. The exact overall component ionization rates calculated by time-averaging of the component IIR are compared with those calculated approximately via the virtual detector method (VD). Details of the time dependent behavior of the outgoing and incoming electron wavepackets of the H$_2^+$ system in intense laser field at sub-femtosecond time scale are studied based on the calculated component IIR. It is shown clearly that the positive (outgoing electron wavepacket) signals of the IIR and its z component are strong and sharp but the negative (returning electron wavepacket) signals of the IIR are smooth and weak. The structure of the $ρ$ component of the IIR has smooth structure. Relation between the R-dependent ionization rate and duration of the ramp of the laser pulse is studied and it is explicitly shown that for internuclear distance R<5.6, when the laser pulse is turned on without a ramp, the first peak of R-dependent ionization rates moves towards the peak of the lower time dependent Floquet quasi-energy state (QES).

physics.atom-ph↗

arXiv2006

Instantaneous ionization rate of H$_2^+$ in intense laser field; Interpretation of the Enhanced Ionization

The fixed-nuclei full dimensional time-dependent Schr ödinger equation is directly solved for H$_2^+$ in the linearly polarized laser field of $I \sim 1.0 \times 10^{14}$W cm$^{-2}$ and $λ\sim 1064 $nm Instantaneous ionization rate has been introduced and calculated by evaluating the instantaneous imaginary energy of the system. It is shown that positive (negative) values of instantaneous imaginary energy of the system represent the incoming (outgoing) instantaneous current of electron. This approach allows us to determine not only the instantaneous intensity but also the instantaneous direction of the electronic current. The transient behavior of the electron wavepacket in intense laser field can thus be probed precisely. Details of the enhanced ionization rates are studied based on the instantaneous ionization rates. This approach gives direct evidence for existence of the effect of charge-resonance-enhanced multiphoton resonances of the quasi-energy states (QES) with excited electronic states at some particular internuclear distances. Finally, Contributions of the individual time dependent Floquet QES to the overall ionization rates are evaluated.

physics.atom-ph↗