An optical lattice is a periodic potential for atoms, created using\ud a standing wave pattern of light. Due to the interaction between\ud the light and the atoms, the atoms are attracted to either the nodes\ud or the anti-nodes of the standing wave, depending on the exact wave\ud lenght of the light. This means that if such a lattice is loaded with\ud a sufficiently high number of ultracold atoms, a periodic array of\ud atoms is obtained, we an interatomic distance of a few tenths of a\ud micrometer. In order to obtain such a high number of cold atoms, one\ud first has to create a so-called Bose-Einstein condensate. \ud \ud When an optical lattice is loaded from a Bose-Einstein condensate,\ud it is possible to create a system in which every atom is in the\ud lowest band of the lattice and there is on average one atom in each\ud lattice site. Because the lattice potential is created with laser \ud light, the depth of the lattice can easily be tuned by changing the\ud intensity of the laser. When the intensity of the laser light is low,\ud the atoms can tunnel from one site to the next. Due to this tunneling,\ud the gas of atoms in the lattice will remain superfluid. However, if \ud the intensity of the laser light is increased to above a certain \ud critical value, a quantum phase transition occurs to a so-called Mott \ud insulator.\ud In this state, the atoms can no longer tunnel due to the fact that \ud the on-site interaction between atoms becomes more important then\ud the tunneling probability. \ud \ud In this PhD thesis, a description is given of the experimental setup\ud that is being constructed in our group to create these systems in our\ud lab. Also, a theoretical description is given of these systems and\ud several important quantities our derived, such as the gap of the \ud Mott-insulating state. Furthermore, an experiment is proposed that can\ud be used to accurately measure this gap
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