Optical periodic potentials (optical lattices) are well-known for being defect-free
and easy to
manipulate. Recent experiments involve loading Bose-Einstein condensates (BECs)
into optical
lattices. This results in a macroscopic quantum system of coherent matter waves whose
properties can
be easily and precisely controlled.
Manipulation of BEC wavepackets in a periodic potential can lead to their localisation,
therefore to the generation of matter-wave solitons.
Ensembles of atoms localised in gaps of the matter-wave band-gap spectrum are called
bright gap solitons while in-band localisation creates
dark solitons ("dips" in the density profiles).
In this project we computationally model the dynamics of a nonlinear localised matter-wave
in one- and two-dimensional optical lattices.
By engineering the properties of the optical lattice we produce bright gap matter-wave
solitons in a Bose-Einstein condensate with repulsive inter-atomic interactions. We study
stability, mobility and interaction of these localised structures,
and also investigate trapping of nontrivial phase states-lattice vortices.
Novel methods for generating trains of gap solitons (series of the localised states)
are explored by employing nonlinear evolution of a periodic matter-wave
triggered by its modulational instability.
To investigate the influence of finite temperature effects, we model the dynamical
generation of the gap soliton train in the presence of
a thermal cloud. In order to do so, we apply the stochastic truncated Wigner method. This
approach allows us to "separate" condensed and uncondensed fractions of atoms.
With this simulations we are able to model increasing loss of atoms from the condensate
to the surrounding thermal cloud at the edge of the Brillouin zone, the so called
anomalous heating.
Methods of optical confinement (e.g. in optical lattices) make the trapping
of cold atoms with spin degree of freedom possible.
Within this project we consider spinor BECs of Rb87 and Na23 atoms trapped in an optical
lattice.
The first one has a ferromagnetic spin-dependent
interaction (i.e. the spins prefer to co-align).
On the other hand, the second is characterised by a anti-ferromagnetic
spin-dependent interaction.
In particular, we analyze the interplay between the periodicity of the lattice
potential and the spin-dependent nonlinearity.
This interplay enables the existence of multi-component (vector)
localised states of the condensate. In the lattice, the spinor states may be
localised as both ferromagnetic and polar spin structures.
In addition, provided an optical confinement, the spin degree of freedom
can be manipulated by an external magnetic field.
In the near future, we intend to explore the dynamical properties of the single-component
and spinor matter-waves gap solitons in their binary interactions in the presence
of vacuum noise.
A further direction is the study of spectra and dynamics of atomic matter-waves
of a Bose-Einstein condensate in quasiperiodic and random lattices
with an aim to determine how the effects of long-range order and disorder would affect
the mobilty and localisation properties of the nonlinear matter-waves.
In addition, we plan to extend our study of quantum properties of lattice solitons
and vortices.