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.
Ultra-cold atoms systems used as quantum simulators offer an alternative way to simulate many-body systemsbehaviour in condensed matter. Indeed, we can create artificial matter with optical lattices : the stationnarywave reproduces the potential wells in the crystalline structure. Moreover, the big advantage of using cold atomsis that the parameters of the simulated crystal can be well controlled so that we can understand the electricaland magnetism properties of the condensed matter such as conductivity, ferromagnetism ...The commonapproach for generating optical lattices is interfering two laser beams in one dimension. The lattice spacing islimited by the interfringe, which is half the wavelength. However, the more the lattice spacing decreases, themore the interaction energies increase [3].In the new ongoing project, we are going to produce subwavelengthlattices by irradiating a nanostructure gold layer. The subwavelength potential is got thanks to the control ofthe interactions between the beams, the atomic cloud, and the nanostructured surface. This system will be ableto study new interaction regimes with very high tunability (different lattice geometries, impurities...).