Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Abstract We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling(SECS)absorbing method and Arnoldi propagation method.Such combination has not been reported in the literature.The proposed scheme is particularly useful in the applications involving long-time wave propagation.The SECS is a wonderful absorber,but its application results in a non-Hermitian Hamiltonian,invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian.We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian.The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet(XUV)and strong infrared(IR)laser pulses.Both perfect absorption and stable propagation are observed.

Extra Time Dimension: Deriving Relativistic Space-Time Transformations, Kinematics, and Example of Dimensional Compactification Using Time-Dependent Non-Relativistic Quantum Mechanics

We consider a five-dimensional Minkowski space with two time dimensions characterized by distinct speeds of causality and three space dimensions. Formulas for relativistic coordinate and velocity transformations are derived, leading to a new expression for the speed limit. Extending the ideas of Einstein’s Theory of Special Relativity, concepts of five-velocity and five-momenta are introduced. We get a new formula for the rest energy of a massive object. Based on a non-relativistic limit, a two-time dependent Schrödinger-like equation for infinite square-well potential is developed and solved. The extra time dimension is compactified on a closed loop topology with a period matching the Planck time. It generates interference of additional quantum states with an ultra-small period of oscillation. Some cosmological implications of the concept of four-dimensional versus five-dimensional masses are briefly discussed, too.

Momentum distributions of symmetric(H_(2)^(+))and asymmetric(HeH^(2+))molecular ions in a circularly polarized laser field under different ionization mechanisms

By numerically solving the two-dimensional(2D)time-dependent Schrödinger equation(TDSE),we present photoelectron momentum distributions(PMDs)and photoelectron angular distributions(PADs)of symmetric(H_(2)^(+))and asymmetric(HeH^(2+))molecular ions in circularly polarized(CP)laser pulses.By adjusting the laser wavelength,two circumstances of resonance excitation and direct ionization were considered.The ionization mechanism of the resonance excitation was mainly investigated.The results show that the PMDs of H_(2)^(+) and HeH^(2+) in the y-direction gradually increase with increasing intensity,and the number of PMDs lobes is in good agreement with the results predicted by the ultrafast ionization model.In the resonance excitation scenario,the PMDs of are dominated by two-photon ionization,whereas the PMDs of HeH_(2)^(+) are dominated by three-photon ionization.Furthermore,the PMDs of HeH^(2+)are stronger in the resonance excitation scenario than those of H_(2)^(+),which can be explained by the time-dependent population of electrons.In addition,the molecular structure is clearly imprinted onto the PMDs.

Two-photon double ionization of helium by chirped few-cycle attosecond pulses:From nonsequential to sequential regime

The two-photon double ionization（TPDI） dynamics of helium by chirped attosecond pulses are theoretically studied by solving the two-electron time-dependent Schr o¨dinger equation in its full dimensions. We show that both the differential and the total double ionization probability can be significantly controlled by adjusting the chirp. The dependence of the TPDI on the chirp can be quite different for different photon energies, relying on the central photon energy being in the sequential region, nonsequential region, or translation region. The physics which lead to the chirp dependence for different photon energies are addressed. Present findings are well reproduced by a model based on the second-order time-dependent perturbation theory.

Photoelectron momentum distributions of Ne and Xe dimers in counter-rotating circularly polarized laser fields

The strong-field ionization of dimers is investigated theoretically in counter-rotating circularly polarized laser fields.By numerically solving the two-dimensional(2D)time-dependent Schrödinger equation(TDSE)with the single-electron approximation(SEA)frame,we present the photoelectron momentum distributions(PMDs)and photoelectron angular distribution(PADs)of aligned Ne and Xe dimers.It is found that the PMDs and PADs strongly depend on the time delays by counter-rotating circularly polarized laser pulses.The results can be explained by the ultrafast photoionization model and the evolution of electron wave packets for Ne and Xe dimers.Besides,We make a comparison of PMDs between Ne atom and Ne dimer.

Calibration of quantitative rescattering model for simulating vortex high-order harmonic generation driven by Laguerre–Gaussian beam with nonzero orbital angular momentum

We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger equation(TDSE).We show that the QRS perfectly agrees with the TDSE under the favorable phase-matching condition,and the QRS can accurately predict the main features in the spatial profiles of vortex HHG if the phase-matching condition is not good.We uncover that harmonic emissions from short and long trajectories are adjusted by the phase-matching condition through the time-frequency analysis and the QRS can simulate the vortex HHG accurately only when the interference between two trajectories is absent.This work confirms that it is an efficient way to employ the QRS model in the single-atom response for precisely simulating the macroscopic vortex HHG.