Modelling laser-atom interactions in the strong field regime

Abstract

We consider the ionisation of atomic hydrogen by a strong infrared field. We extend and study in more depth an existing semi-analytical model. Starting from the time-dependent Schrödinger equation in momentum space and in the velocity gauge we substitute the kernel of the non-local Coulomb potential by a sum of N separable potentials, each of them supporting one hydrogen bound state. This leads to a set of N coupled one-dimensional linear Volterra integral equations to solve. We analyze the gauge problem for the model, the different ways of generating the separable potentials and establish a clear link with the strong field approximation which turns out to be a limiting case of the present model. We calculate electron energy spectra as well as the time evolution of electron wave packets in momentum space. We compare and discuss the results obtained with the model and with the strong field approximation and examine in this context, the role of excited states.

Ionisation of H 2 O by a strong ultrashort XUV pulse: a model within the single active electron approximation

“…For the sake of completeness, it is important to mention that our approach is not gauge invariant as it is the case for most of the approximate treatments. The problem of the gauge and the delicate question of the possible existence of a privileged gauge are discussed in detail in the context of the present model by Galstyan et al 9 The problem of the interaction of the water molecule with a femtosecond or sub femtosecond XUV pulse has almost never been treated theoretically up to now. As far as we know, most of the theoretical calculations have been performed at a wave length of 800 nm.…”

“…For the sake of clarity, we first consider briefly the case of atomic hydrogen. Details of the calculations are found in Galstyan et al 9 We then show, in more detail, how it can be generalized to a more complex system such as the water molecule.…”

“…The problem of the gauge invariance in the context of nonlocal potentials has been discussed in great detail in various references. 9,17,18 In particular, it is shown in 9 that it is possible to formulate our separable potential model in various ways that can be grouped into two families such that within a given family, the length and velocity gauge formulations give the same value for the observables. This shows clearly the non-existence of a privileged gauge but does not solve the problem of the "global" gauge invariance since formulations belonging to the first and the second family give different results for the observables.…”

Many particle spectroscopy of atoms, molecules, clusters and surfaces: international conference MPS-2016

“…Besides already mentioned work [33], this issue contains other articles in this field [58][59][60]. Two of them develop methods of solution of the time-dependent Schrödinger equation (TDSE), which is currently a very important field of theory in view of applications to interaction of short radiation pulses with matter.…”

“…Thus the method promises good perspectives. In [59] the same group uses separable potential method and performs very extensive analysis of the results for ionization of hydrogen atom by strong low-frequency field. In this method, the TDSE in the momentum space reduces to a set of coupled one-dimensional linear Volterra integral equations.…”