Dynamic evolution of spin-1 and spin-2 dipolar BECs
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This study investigates the dynamical evolution of spin-1 and spin-2 Bose-Einstein Condensates (BECs) when the dipolar interaction is taken into consideration. Using the Single-Mode Approximation (SMA) equations of motion are derived for each condensate component which are then numerically solved. The results convincingly show that the dipolar interaction has a significant effect despite being much weaker than the collision or spin-exchange interaction and that if included magnetic effects are easy to treat. Further, an analytical Mean-Field Theory formulation is used to derive and simplify equations of motion for a spin-1 BEC in 2D (pancake) configuration. Moving to a reference frame that rotates at the Larmor frequency greatly simplifies the equations and removes first-order Zeeman terms, rendering the effects of the dipolar interaction much clearer to observe in the condensate evolution.
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Tsekouras, Konstantinos. "Dynamic evolution of spin-1 and spin-2 dipolar BECs." (2007) Master’s Thesis, Rice University. https://hdl.handle.net/1911/103674.