Dynamics of bright solitons in
Bose–Einstein condensates:
investigations of soliton behaviour
in the vector Gross–Pitaevskii
equation and applications to
enhanced matter-wave
interferometry

Abstract

Bright solitons in a quasi-1D Bose–Einstein condensate can be used to enhance
precision in matter-wave interferometry, due to their inherent robustness and
support against dispersion. Such a soliton interferometer typically relies on a
potential barrier used to split a single soliton into two smaller coherent solitons
which can then be recombined on the same barrier. In this thesis we examine
two extensions to this scheme. Firstly, we investigate a binary BEC system consisting of two bright solitons which are coupled through a mutual nonlinear interaction term. We derive a set of conditions under which the two components
can be separated on a potential barrier and use numerical simulations to probe
the regimes beyond which this mathematical treatment is applicable. We then
use the numerical simulations to look at the effect of the nonlinear coupling on
the dynamics of the binary solitons interacting with the barrier. We also look
at the interference behaviour found by doubling the simulation time in either
a ring trap or a harmonic trapping potential (to ensure recombination on the
barrier); as well as the case where the solitons start spatially separated on either
side of the barrier in order to find conditions under which the solitons will combine on the barrier. We find a good agreement between the analytical predictions and the results of simulations. Beyond the regions of parameter space
where the predictions are expected to hold, we find complex transmission and
interference behaviour as a result of nonlinear effects. The second part of this
thesis consists of an examination of the prospect of using a subwavelength barrier scheme in a soliton interferometry experiment. This involves using two
resonant coupling beams in a Λ-system with a spatially varying intensity. Under certain conditions, this can be used to form an effective potential barrier
with a width which is not diffraction-limited. We look at suitable parameter regimes for such a barrier to split and recombine solitons in an interferometer
and probe the effects of possible complications such as misalignment in the
beams and different scattering lengths in the different states. We simulate the
soliton interferometer using the full three component GPE as well as the single
component analogue with the effective potential in order to characterise the
soliton behaviour and the dependence of the interferometer sensitivity on the
system parameters. We find a trend towards an idealised soliton interferometer
with a decreasing value of the parameter, w, controlling the barrier characteristics. Also, we demonstrate an agreement between the relevant three component GPE and the analogous single component GPE, in the limit of strong
coupling fields.