Application of a numerical-basis-state method to strong-field excitation and ionization of hydrogen atoms

Abstract

We apply a numerical-basis-state method to study dynamical processes in the interaction of atoms with strong laser pulses. The method is based on the numerical representation of finite-space energy eigenstates of the field-free atomic Hamiltonian in a box on a grid and the expansion of the solution of the full time-dependent Schrödinger equation, including the interaction with the field, in this numerical basis. We apply the method to the hydrogen atom and present results for excitation and ionization probabilities as well as photoelectron momentum distributions. Convergence of the results with respect to the size of the basis as well as the parallel efficiency of the numerical algorithm is studied. The results of the numerical-basis-state method are in good agreement with those of two-dimensional numerical grid calculations. The computation times for the numerical-basis-state method usually are found to be significantly smaller than those for the two-dimensional grid calculations, whereas, even higher excited states can be well represented. We further apply this method to study a few recently reported phenomena related to strong-field excitation of atoms, such as the dependence of the excitation probabilities on the carrier-envelope phase in ultrashort pulses as well as the so-called frustrated ionization.

Attosecond transient absorption probing of electronic superpositions of bound states in neon: detection of quantum beats

“…For a more complete theoretical picture, the many-level time-dependent Schrödinger equation (TDSE) is solved by expanding it in a basis of numerically calculated basis states [29]. The field-free atomic energies and dipole moments are calculated using the GRASP package [30], which solves the multi-configuration Dirac-Fock equation.…”

Strong-Field Excitation of Helium: Bound State Distribution and Spin Effects

“…The frustrated tunneling ionization (FTI) process, a recently established im portant exit channel o f an extended version o f the simple m an's or rescattering m odel, in w hich the C oulom b field is consid ered explicitly, predicts the n distribution o f excited states in the tunneling regim e o f strong-field ionization [20,22]. W hile these predictions are backed up by quantum m echanical calculations [20,23], the experim ental confir m ation, which w ould put the idea o f describing excitation within the tunneling m odel on solid ground, is still pending.…”

Transition from perturbative to nonperturbative interaction in low-order-harmonic generation

“…The radial wave functions are obtained as numerical solutions of the corresponding eigenvalue equation for the radial field-free time-independent Schrodinger equation using the Numerov method on a logarithmic one-dimensional finitespace grid of size Rq with boundary conditions rR " i(r)|r=o = r Rni(r )\r=R0 = 0 [13]. Due to the finite size of the box the num ber o f bound states is lim ited, and the continuum is discretized.…”

“…n,l,n ' ,v and propagate the tim e-dependent S chodinger equation using the C rank-N icholson m ethod [13],…”

“…(1) does not converge at intensities above about 2 x 1013 W /cm 2 since the magnitudes of the higher-order terms do exceed a significant fraction of the lowest-order non linear term. The calculations of the higher-order coefficients were performed using a numerical basis-state method [13], which also enabled us to determine the nonlinear electrical susceptibility from the ab initio solution of the corresponding Schrodinger equation. Comparison of the results of both kinds of calculations let us conclude that a change in the intensity dependence of the susceptibility has to be interpreted as PACS number(s): 32.80.Wr, 42.65.An, 42.65.Ky a signature of the nonperturbative interaction between the intense laser light and the gas, whereas perturbative concepts, such as HOKE, are not applicable.…”