Off-axis Vortex in a Rotating Dipolar Bose-Einstein Condensation

We consider a singly quantized off-axis straight vortex in a rotating dipolar ultracold gas in the Thomas-Fermi (TF) regime. We derive analytic results for small displacements and perform numerical calculations for large displacement within the TF regime. We show that the dipolar interaction energy increases (decreases) as the vortex moves from the trap center to the edge in an oblate (a prolate) trap. We find that for an oblate (a prolate) trap, the effect of the dipole-dipole interaction is to lower (raise) both the precession velocity of an off-center straight vortex line and the angular velocity representing the onset of metastability.