A Schr\"{o}dinger equation for relativistic laser-matter interactions

A semi-relativistic formulation of light-matter interaction is derived using the so called propagation gauge and the relativistic mass shift. We show that relativistic effects induced by a super-intense laser field can, to a surprisingly large extent, be accounted for by the Schr{\"o}dinger equation, provided that we replace the rest mass in the propagation gauge Hamiltonian by the corresponding time-dependent field-dressed mass. The validity of the semi-relativistic approach is tested numerically on a hydrogen atom exposed to an intense XUV laser pulse strong enough to accelerate the electron towards relativistic velocities. It is found that while the results obtained from the ordinary (non-relativistic) Schr{\"o}dinger equation generally differ from those of the Dirac equation, merely demonstrating that relativistic effects are significant, the semi-relativistic formulation provides results in quantitative agreement with a fully relativistic treatment

Relativistic effects in photoionizing a circular Rydberg state in the optical regime

We study the photoionization process of a hydrogen atom initially prepared in a circular Rydberg state. The atom is exposed to a two-cycle laser pulse with a central wavelength of 800 nm. Before the atom approaches saturation, at field intensities of the order of 10 17 W / cm 2 , relativistic corrections to the ionization probability are clearly seen. The ionization is predominantly driven by the radiation pressure in the propagation direction of the laser field, not by the electric field. Direct comparisons with the full numerical solution of the time-dependent Dirac equation demonstrate quantitative agreement with a semirelativistic approximation, which is considerably easier to implement.publishedVersio

Relativistic light-matter interaction

During the past decades, the development of laser technology has produced pulses with increasingly higher peak intensities. These can now be made such that their strength rivals, and even exceeds, the atomic potential at the typical distance of an electron from the nucleus. To understand the induced dynamics, one can not rely on perturbative methods and must instead try to get as close to the full machinery of quantum mechanics as practically possible. With increasing field strength, many exotic interactions such as magnetic, relativistic and higher order electric effects may start to play a significant role. To keep a problem tractable, only those effects that play a non-negligible role should be accounted for. In order to do this, a clear notion of their relative importance as a function of the pulse properties is needed.  In this thesis I study the interaction between atomic hydrogen and super-intense laser pulses, with the specific aim to contribute to the knowledge of the relative importance of different effects. I solve the time-dependent Schrödinger and Dirac equations, and compare the results to reveal relativistic effects. High order electromagnetic multipole effects are accounted for by including spatial variation in the laser pulse. The interaction is first described using minimal coupling. The spatial part of the pulse is accounted for by a series expansion of the vector potential and convergence with respect to the number of expansion terms is carefully checked. A significantly higher demand on the spatial description is found in the relativistic case, and its origin is explained. As a response to this demanding convergence behavior, an alternative interaction form for the relativistic case has been developed and presented. As a guide mark for relativistic effects, I use the classical concept of quiver velocity, vquiv, which is the peak velocity of a free electron in the polarization direction of a monochromatic electromagnetic plane wave that interacts with the electron. Relativistic effects are expected when vquiv reaches a substantial fraction of the speed of light c, and in this thesis I consider cases up to vquiv=0.19c. For the present cases, relativistic effects are found to emerge around vquiv=0.16c

Relativistic photoionization with elliptically polarized laser fields in the ultraviolet region

An alternative and powerful Schrödinger-like equation for describing beyond dipole laser-matter interactions is derived. It is shown that this particular formulation is numerically very efficient with respect to computational effort and convergence rate of the solutions. Furthermore, and more importantly, its nonrelativistic form turns out to be more compatible with relativity than what seems to be the case with the more common formulations of the nonrelativistic light-matter interaction. Moreover, an extension of this interaction form into the relativistic region preserves, to a large extent, the numerical efficiency

Semirelativistic Schrödinger Equation for Relativistic Laser-Matter Interactions

A semirelativistic formulation of light-matter interaction is derived using the so called propagation gauge and the relativistic mass shift. We show that relativistic effects induced by a superintense laser field can, to a surprisingly large extent, be accounted for by the Schrödinger equation, provided that we replace the rest mass in the propagation gauge Hamiltonian by the corresponding time-dependent field-dressed mass. The validity of the semirelativistic approach is tested numerically on a hydrogen atom exposed to an intense extreme ultraviolet laser pulse strong enough to accelerate the electron towards relativistic velocities. It is found that while the results obtained from the ordinary (nonrelativistic) Schrödinger equation generally differ from those of the Dirac equation, demonstrating that relativistic effects are significant, the semirelativistic formulation provides results in quantitative agreement with a fully relativistic treatment

Relativistic effects in photoionizing a circular Rydberg state in the optical regime

We study the photoionization process of a hydrogen atom initially prepared in a circular Rydberg state. The atom is exposed to a two-cycle laser pulse with a central wavelength of 800 nm. Before the atom approaches saturation, at field intensities of the order of 1017 W/cm2, relativistic corrections to the ionization probability are clearly seen. The ionization is predominantly driven by the radiation pressure in the propagation direction of the laser field, not by the electric field. Direct comparisons with the full numerical solution of the timedependent Dirac equation demonstrate quantitative agreement with a semi-relativistic approximation, which is considerably easier to implement

Relativistic effects in photoionizing a circular Rydberg state in the optical regime

We study the photoionization process of a hydrogen atom initially prepared in a circular Rydberg state. The atom is exposed to a two-cycle laser pulse with a central wavelength of 800 nm. Before the atom approaches saturation, at field intensities of the order of 10 17 W / cm 2 , relativistic corrections to the ionization probability are clearly seen. The ionization is predominantly driven by the radiation pressure in the propagation direction of the laser field, not by the electric field. Direct comparisons with the full numerical solution of the time-dependent Dirac equation demonstrate quantitative agreement with a semirelativistic approximation, which is considerably easier to implement