Towards quantum simulation with atoms trapped in magnetic nanolattices on a chip

In the context of quantum simulation and quantum information, steps were made to push forward the study of complex systems and the development of quantum technology. Our idea of quantum simulators consists of ultracold atoms trapped in magnetic nanolattices on a chip. The thesis starts with providing the framework to design magnetic microtraps, starting from the simplest one-dimensional case and extends the problem to 2D lattices. This introduction is followed by the demonstration how to realize a quantum simulator to study the Mott-insulator to superfluid transition using atoms that are magnetically trapped above a chip surface. The calculation is done for 2D square, symmetric lattices with two different spacings: 425 nm and 200 nm. The first example is used to compare our theoretical result to the experimental result achieved with optical lattices with the same lattice spacing. The second example demonstrates that we can observe the quantum phase transition between a Mott-insulator and a superfluid for small lattice constants, which is challenging to reach for optical systems and has never been done experimentally. The thesis continues discussing the Magchips Nano experiment and the characterization of the experimental steps made towards the loading of the atoms on the chip. The final part of this thesis is dedicated to a project made in collaboration with a group at the ETH in Zurich about "magic" Rydberg-Rydberg transitions for ³⁹K, which creates atoms that are extremely sensitive for each other and rather insensitive for their environment.