The Time Dependent Schrödinger Equation In A Strong Laser Field
Creators: name: Böhme, Maximilian
Publisher: name: Zenodo
Year: 2016

description: Laser-matter interaction is one of the main topics in current physical research, due to the fact<br>
that lasers enable the study of matter under various physical conditions. For instance the<br>
interactions of lasers with plasmas, solid state matter as well as warm dense matter (WDM) are<br>
currently vivid research subjects. Laser interactions not only extended our understanding of<br>
matter itself, it also opens up possibilities for a wide range of applications. Cheaper and more<br>
effective cancer therapy and laser particle acceleration are promising outlooks [1, 2].<br>
Lasers are also utilized to create WDM. For the production of WDM, laser shock waves are shot<br>
at a target, which will create highly compressed states of mega-bar pressures and temperatures on<br>
a scale of several electron volts [3, 4]. To probe WDM, lasers can be used for wide or small angle<br>
x-ray scattering analysis, also absorption spectroscopy and many other applications regarding<br>
this subject. Laser-driven plasma acceleration does not only hold a potential application to<br>
medical treatments, but in the area of material science, where lasers could facilitate a deeper<br>
implantation of multiple ion species in semiconductors [5]. In nuclear fusion research, lasers can<br>
compress the fusion pellet directly or indirectly. Ignition of the fusion reaction is then possible<br>
either due to the shock conditions or a additional external driver like electron or ion beams,<br>
which themselves are accelerated using powerful lasers [5]. A different, yet powerful, laser concept<br>
is the free-electron laser (FEL). The basic principle of FELs is the emittance of synchrotron<br>
radiation from relativistic electrons by sending them into an undulator. Thus, the electrons start<br>
to oscillate and emit light down to wavelengths on the x-ray spectrum [6]. FELs capable of<br>
emitting such wavelengths are called XFELs. Those kind of FELs are not only of interest in<br>
physical research, but also find applications in e.g. biological research [7]. Facilities featuring<br>
such XFELs are for instance the Lineac Coherent Light Source (LCLS) in Stanford [8] or, by the<br>
end of 2016, the European XFEL facility at DESY in Hamburg [9]. Usual laser concepts can be<br>
grouped, by the length of their emitted pulses, into ultra-short and long-pulse lasers. An example<br>
of an ultra-short pulse laser is the Dresden laser acceleration source (DRACO) at the Helmholtz<br>
Zentrum Dresden Rossendorf (HZDR) [10]. These kind of lasers are often deployed for laser<br>
particle acceleration research. Long-pulse lasers are used for the ignition of plasmas, as in the<br>
NIF facility. Other examples for long-pulse lasers are the n- and phelix [11, 12] at the GSI in<br>
Darmstadt or the Orion laser in Aldermaston [13]. The scale of those long laser pulses is about<br>
several nanoseconds, whereas short-pulse lasers have typical pulse lengths of several femtoseconds.<br>
The physical effects of laser matter interaction include the creation of Auger electrons, where a<br>
laser pulse pulls out an inner shell electron and causes the relaxation of an outer shell electron to<br>
the unoccupied energy level. This relaxation causes the emission of another electron, the so called<br>
Auger electron, without the emittance of any radiation [14]. The Auger electron effect already<br>
shows that lasers are able to ionize atoms, where an electron essentially becomes free through the<br>
interaction with a laser field. This can lead to further effects like the recombination of electrons<br>
with ions, which can cause the emission of photons as the so called radiative recombination.<br>
Lasers also are able to interact with free electrons by inelastic scattering. Electrons can get<br>
excited to higher energy levels by inelastic laser scattering, afterwards this excited state relaxes<br>
into its initial energy level by the emission of a photon [14]. In addition to all those bound<br>
electron laser interactions as examples of inelastic scattering, elastic scattering of bound electrons<br>
is possible as well. A large part of the x-ray scattering spectrum is the elastic peak, which is<br>
caused by elastic interactions of bound electrons with x-ray wavelength photons. This means,<br>
5that bound electrons oscillate in the laser field and emit light of the same frequency. That is the<br>
case, if the photon energy does not match the transition energy. In general, laser emissions are<br>
able to lift bound states to higher energy levels. Furthermore lasers enable lowering of potential<br>
barriers, enabling a bound particle to tunnel trough [15]. All of those effects are experimentally<br>
observed and broaden our knowledge about matter. Measurements of these physical effects are<br>
standard nowadays. However, it is very challenging to temporally resolve the processes, as they<br>
happen on atto- to femto-second time scales. Simulating those physical processes enables us to<br>
see the fundamental process behind experimental observations, and enhance the way theory and<br>
experiment complement each other. Especially, effects like ionization or state transitions are only<br>
well understood, if one is able to exactly explain what is happening and how well the theory<br>
behind those processes predict the experimental outcome on those microscopic scales . As one<br>
tries to explain a non relativistic quantum mechanical system, the starting point of all models is<br>
the Schrödinger Equation. Thus, the main subject of this thesis is to find a general way to<br>
simulate a one-dimensional quantum system in a strong time-dependent potential.