We theoretically investigate high-order harmonic generation and attosecond pulses by numerically solving the three-dimensional time-dependent Schr\"odinger equation from a helium ion in a two-color laser field, which is synthesized by adding a 1600-nm laser pulse to a multicycle 800-nm laser pulse. The numerical results show that the short quantum path selection and broadband continuum spectra are achieved by adjusting the relative phase between two laser pulses, and isolated attosecond pulses can be generated successfully. Compared with the case of He${}^{+}$ ions from the 1$s$ ground state, the emission efficiency of the continuous harmonics and the intensity of the isolated attosecond pulse are enhanced approximately thirteen orders of magnitude by preparing He${}^{+}$ ions in a coherent superposition of the states 1$s$ and 2$s$. Furthermore, the bandwidth of the continuum spectrum is further broadened by increasing the intensity of the 1600-nm laser pulse, and an intense 38-as isolated pulse with a bandwidth of 109 eV is straightforwardly obtained.

Generation of intense isolated sub-40-as pulses from a coherent superposition state by quantum path control in the multicycle regime

We theoretically propose a three-color laser scheme to enhance the high-order harmonic intensity and generate an isolated attosecond pulse. By adding a 3 fs, 1600 nm laser pulse to a synthesized two-color laser field (5 fs, 800 nm and 10 fs, 1200 nm), the harmonic intensity is effectively enhanced and an isolated attosecond pulse with duration 41 as is generated. In this scheme, the short trajectory is suppressed, the selection of the long quantum path can be achieved. We also investigate emission time of harmonics in terms of the time-frequency analysis and the semi-classical three-step model to illustrate the physical mechanism of high-order harmonic generation.

https://link.springer.com/content/pdf/10.1134%2FS1054660X12110035.pdf

The control of the electron quantum paths for the generation of isolated attosecond pulse using a three-color laser scheme

We investigate the elliptical high-order harmonic generation (HHG) from the ground state of H+2 subjected to linearly polarized laser fields, by numerically solving the three-dimensional (3D) time-dependent Schrodinger equation (TDSE) and using the strong-field approximation (SFA) models. Highly elliptical HHG is yielded at intermedial alignment angles from the TDSE, while the standard SFA model fails to predict this. By including the coulomb potential and the stark shift corrections, we yield qualitative agreement results with the TDSE. The comparisons show that in the description of elliptical HHG, both the coulomb potential and the stark-shift are necessary.

Elliptical High-Order Harmonic Generation from H + 2 in Linearly Polarized Laser Fields

A very simple and highly accurate method of investigating the behavior of atomic system in a strong magnetic field has been developed based on the generalized pseudospectral discretization. As examples, we present the calculations of the binding energies and quadruple moments for the ground and low-lying excited states of the hydrogen atom in a magnetic field ranging from zero up to 1000 a.u.. The obtained results are found to be in excellent agreement with other high-accuracy theoretical calculations. The present method may be straightforwardly applied to cross electric-magnetic field in an arbitrary orientation.

Calculations of low-lying states of hydrogen atom in strong magnetic field by generalized pseudospectral method

By solving a time-dependent Schrodinger equation (TDSE), we studied the electron capture process in the He2 + +H collision system under a strong magnetic field in a wide projectile energy range. The strong enhancement of the total charge transfer cross section is observed for the projectile energy below 2.0 keV/u. With the projectile energy increasing, the cross sections will reduce a little and then increase again, compared with those in the field-free case. The cross sections to the states with different magnetic quantum numbers are presented and analyzed where the influence due to Zeeman splitting is obviously found, especially in the low projectile energy region. The comparison with other models is made and the tendency of the cross section varying with the projectile energy is found closer to that from other close coupling models.

https://iopscience.iop.org/article/10.1088/1674-1056/24/9/093402/pdf

Charge transfer of He 2 + with H in a strong magnetic field

We present an accurate and efficient generalized pseudospectral method for solving the time-dependent Schrodinger equation for atomic systems interacting with intense laser fields. In this method, the time propagation of the wave function is calculated using the well-known second-order split-operator method implemented by the numerically exact, fast transform between the grid and spectral representations. In the grid representation, the radial coordinate is discretized using the Coulomb wave discrete variable representation (CWDVR), and the angular dependence of the wave function is expanded in the Gauss–Legendre–Fourier grid. In the spectral representation, the wave function is expanded in terms of the eigenfunctions of the field-free zero-order Hamiltonian. Calculations on the high order harmonic generation and ionization dynamics of hydrogen atom in strong laser pulses are presented to demonstrate the accuracy and efficiency of the present method. This new algorithm will be found more computationally attractive than the close-coupled wave packet method using CWDVR and/or methods based on evenly spaced grids.

https://iopscience.iop.org/article/10.1088/0256-307X/26/5/053202/pdf

Generalized Pseudospectral Method for Solving the Time-Dependent Schrödinger Equation Involving the Coulomb Potential

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Generalized Pseudospectral Method for Solving the Time-Dependent Schrödinger Equation Involving the Coulomb Potential