Tools and fundamental techniques for Bose-Einstein condensate microscopy

Ultra-cold atoms have small kinetic energy and are therefore very sensitive to external fields that act on the atoms. By having fine control over the positioning of the ultra-cold atom cloud we can use the atom cloud as a sensor for magnetic fields. By imaging these atom clouds we can infer a spatial map of the magnetic field. This spatial map will have a resolution proportional to the distance between the source of the magnetic field and the atom cloud which can be on the order of 0:1 µm. In the first half of the thesis, we investigate the two colour magneto-optical trap. This is a simple technique that can lead to a multiplicative increase in the number of atoms in a magneto-optical trap with a simple change to the optical setup. Using the two colour magneto-optical trap we have observed an increase of 5 times in the number of trapped atoms. An increase in the number of atoms in a magneto-optical helps with later cooling processes that are not lossless such as evaporative cooling which in turn helps the realisation of the ultra-cold atom microscope. In the second half of the thesis, we demonstrate how a 2d current density can be recovered from a 2d magnetic field map generated by the ultra-cold atom microscope. We then go on to show the sensitivity and responsivity of a cold atom cloud and a Bose-Einstein condensate. We then use the results of the previous section to simulate the measurement of currents in a silver nanowire network. Properties of the silver nanowire network can be simulated and aid in showing the abilities and limitations of the ultra-cold atom microscope. We found that the ultra-cold atom microscope can directly measure currents in low-density silver nanowire networks. In a high-density silver nanowire network, the average distance between the wires becomes too small to resolve. Hot-spots, areas of high current density can still be identified using the ultra-cold atom microscope. The ultracold atom microscope could then be used as a tool to aid the research look to use silver nanowires in many industrial applications such as touch screens.