We model the dynamics of condensation in a bimodal trap, consisting of a large reservoir region, and a tight dimple whose depth can be controlled. Experimental investigations have found that such dimple traps provide an efficient means of achieving c
ondensation. In our kinetic equations, we include two- and three-body processes. The two-body processes populate the dimple, and lead to loss when one of the colliding atoms is ejected from the trap. The three-body processes produce heating and loss. We explain the principal trends, give a detailed description of the dynamics, and provide quantitative predictions for timescales and condensate yields. From these simulations, we extract optimal parameters for future experiments.
We use variational methods to study a spin impurity in a 1D Bose lattice gas. Both in the strongly interacting superfluid regime and the Mott regime we find that the impurity binds with a hole, forming a polaron. Our calculations for the dispersion o
f the polaron are consistent with recent experiments by Fukuhara et. al. [Nature Phys. 9, 235 (2013)] and give a better understanding of their numerical simulations. We find that for sufficiently weak interactions there are ranges of momentum for which the polaron is unstable. We propose experimentally studying the stability of the polaron by measuring the correlation between the impurity and holes. We also study two interacting impurities, finding stable bipolarons for sufficiently strong interactions.
