Abstract
Experiments have been conducted observing Anderson localisation in a two-dimensional ultracold gas. The atomic transport of a Rb87 Bose-Einstein condensate through a dumbbell shaped optical trap was examined, with a connecting channel containing impurities providing the only path. We have utilised a synthetic gauge field to demonstrate, theoretically, negative magneto-resistance in systems comparable to these experiments. This pro- vides us with strong evidence for the existence of Anderson localisation, an intriguing interference phenomenon, in these systems. Similar systems are examined with impurities distributed periodically, contrasting the ran- dom distributions required for Anderson localisation. It is demonstrated, through a comparison to the periodic case, that the negative magneto- resistance observed must be the result of the destruction of Anderson local- isation. Corresponding localisation lengths are also examined. We see that under that application of a synthetic gauge field, localisation lengths in- crease. A BEC localised within the channel can become delocalised on that scale with the application of a synthetic gauge field, with the correspond- ing localisation length transitioning from smaller than the channel length to larger. Experimental verification of our theoretical predictions would provide strong evidence confirming the existence of Anderson localisation in the experiments.