Since the experimental achievement of Bose-Einstein condensation (BEC) in dilute gases, ultra-cold atom systems have proven to be an unparalleled test bed for condensed matter phenomena. With this in mind, our laboratory set out to build an apparatus for the study of the effects of disorder on condensed matter phase transitions using a BEC loaded into one, two, and three-dimensional lattices. My thesis is divided into two main sections. In the first section I describe in detail the design and construction of our apparatus. Our system is designed to form ⁸⁷Rb condensates of approximately 10 ⁵ atoms. We have three possible experimental science chambers. (1) One can perform 1D lattice experiments in the chamber where the condensate is formed. There is a mirror located in vacuum, which is suitable for this purpose. (2) In a glass chamber one can do 1D, 2D, or 3D lattice experiments. Atoms are loaded into a dipole trap (optical tweezer) prior to condensation and transported approximately 20 cm to the glass cell where optical evaporation is performed to form a BEC. (3) One can transfer, using the same techniques as (2), to a chamber with a multi-channel plate detector for Rydberg atom experiments.

The experimental results described in my thesis pertain to situation (1) However, I describe some details of (2) in the construction section. The first experiment presented in my thesis demonstrates the effect of disorder on the time-dependent dynamics of lattice systems. We observe that a small perturbation produces a dramatic change in the adiabaticity criteria for loading a BEC into one-dimensional optical lattice. I conclude with experiments that we expect to perform on this apparatus.