|dc.description.abstract||The interplay of particle and resonant wave scattering including nonlinear effects
creates systems of diverse and interesting quantum many-body physics. A better
understanding of the physics in these systems could lead to new and exiting
application exploiting their quantum nature.
As an example, in this thesis we investigate the scattering of bright matter-wave
solitons in ultracold gases on a square well in one spatial dimension. For this, solutions
of the mean-field Gross-Pitaevskii approximation and a full quantum manybody
method, the so-called multiconfigurational time-dependent Hartree approach
(MCTDH), are compared.
The MCTDH method is based on a finite basis set expansion, which naturally
leads to errors in system properties, such as energies and densities, when compared
to exact results. In this thesis, we propose an efficient solution to this problem
by rescaling the interaction strength between the particles. Even for very large
interactions in the Tonks-Girardeau limit, the rescaling leads to significant improvements.
This is validated by successfully applying the rescaling to problems
in ring systems as well as external confinements, such as a harmonic well and a
The MCTDH method is then applied to the soliton scattering problem and
compared to results from mean-field calculations. The latter verify that solitons,
when scattered on a well, show quantum effects, such as reflection. For the first
time, we show that a soliton can be additionally permanently trapped by the well
due to resonances with bound states.
For this thesis, to extend these results to a full many-body approach, we developed
QiwiB. It is a program package implementing the MCTDHB method,
which is a derivative of the MCTDH method, but optimised for bosonic systems.
Limits for the validity of the MCTDHB approach are addressed by convergence
studies on the soliton scattering problem. Furthermore, we demonstrate that the
scattering on the well enables the creation of macroscopic binary quantum superposition
states, i.e. NOON states. Novel NOON states corresponding to a
superposition of a reflected soliton and a trapped soliton are observed. These
states are shown to exist for a large range of initial conditions, and a possible
experimental realisation is discussed.||en_US