MEAN-FIELD STUDIES OF DIPOLAR BOSE-EINSTEIN CONDENSATES

Thesis (Ph.D.), Department of Physics and Astronomy, Washington State UniversityThe behavior of polarized dipolar Bose-Einstein condensates (BECs) in a harmonic trap has been extensively studied in the mean-field approximation. Mean-field studies show that, in contrast to $s$-wave interacting BECs, both the mechanical and dynamical behaviors of dipolar BECs depend critically on the trap geometry. Exotic ground state densities and collapse dynamics have been predicted for dipolar BECs in a moderately pancake-shaped trap. These behaviors of dipolar BECs are attributed to the long-range and anisotropic nature of the dipole-dipole interaction, which was first observed in 2005 in a BEC of $^{52}$Cr atoms [see Griesmaier \emph{et al.}, PRL {\bf{94}}, 160401 (2005)]. This thesis discusses theoretical mean-field studies of polarized dipolar BECs loaded into a double-well type external confinement, which is characterized by three parameters: the trap aspect ratio, the barrier height and the barrier width. First, we study the properties of a purely dipolar BEC in a double-well potential as a function of the trap aspect ratio by numerically solving the Gross-Pitaevskii and Bogoliubov de Gennes equations. We find that the cigar-shaped geometry supports macroscopic quantum self-trapped states and analyze the Josephson type oscillations using a two-mode model. Dipolar gases in pancake-shaped traps with moderate aspect ratio support structured ground state densities and collapse through a radial or an angular roton mode, depending on the structure of the ground state density. We find that the properties of these systems can be tuned by dividing the trap along the tight confinement direction. In particular, we find an instability island in an otherwise stable region in the phase diagram. Lastly, we vary the separation between the two pancake-shaped wells in the strongly confined direction and describe the system by two independent but coupled wave functions. We find that the properties of a dipolar BEC is affected by the presence of a second dipolar BEC, even if the two BECs are not overlapping spatially. The system destabilizes dramatically for separations below a critical separation. We also study the system behavior using a separable wave function approach, and find that this approach is inadequate to describe the dynamics of the system.Department of Physics, Washington State Universit