The properties of BoseEinstein condensates can be studied and controlled effectively when trapped in optical lattices formed by two counterpropagating laser beams. The dynamics of BoseEinstein condensates in optical lattices are welldescribed by a continuous model using the GrossPitaevskii equation in a modulated potential or, in the case of deep potentials, a discrete model using the Discrete Nonlinear Schrodinger equation. Spatially localised modes, known as lattice solitons in the continuous model, or discrete breathers in the discrete model, can occur and are the focus of this thesis. Theoretical and computational studies of these localised modes are investigated in three different situations. Firstly, a model of a BoseEinstein condensate in a ring optical lattice with atomic dissipations applied at a stationary or at a moving location on the ring is presented in the continuous model. The localised dissipation is shown to generate and stabilise both stationary and traveling lattice solitons. The solutions generated include spatially stationary quasiperiodic lattice solitons and a family of traveling lattice solitons with two intensity peaks per potential well with no counterpart in the discrete case. Collisions between traveling and stationary lattice solitons as well as between two traveling lattice solitons display a dependence on the lattice depth. Then, collisions with a potential barrier of either travelling lattice solitons or travelling discrete breathers are investigated along with their dependence on the height of the barrier. Regions of complete reection or of partial reflection where the incoming soliton/breather is split in two, are observed and understood interms of the soliton properties. Partial trapping of the atoms in the barrier is observed for positive barrier heights due to the negative effective mass of the solitons/breathers. Finally, two coupled discrete nonlinear Schrodinger equations can describe the interaction and collisions of breathers in twospecies BoseEinstein condensates in deep optical lattices. This is done for two cases of experimental relevance: a mixture of two ytterbium isotopes and a mixture of Rubidium (87Rb) and Potassium(41K) atoms. Depending on their initial separation, interaction between stationary breathers of different species can lead to the formation of symbiotic localised structures or transform one of the breathers from a stationary one into a travelling one. Collisions between travelling and stationary discrete breathers composed of different species are separated in four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is suffciently large and repulsive.
Date of Award  25 May 2018 

Original language  English 

Awarding Institution   University Of Strathclyde


Sponsors  EPSRC (Engineering and Physical Sciences Research Council) 

Supervisor  GianLuca Oppo (Supervisor) & Gordon Robb (Supervisor) 
