Manifestations of the roton mode in dipolar Bose-Einstein condensates

We investigate the structure of harmonically trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that even a small perturbation in the trapping potential can lead to dramatic changes in the condensate's density profile for sufficiently large dipolar interaction strengths and trap aspect ratios. By employing a generalized perturbation theory, we relate these oscillations to a previously-identified ``roton-like'' mode that is believed to exist in dipolar BECs~\footnotemark[1]. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been reported previously~\footnotemark[2]. \footnotetext[1]{\hspace{1pt} S. Ronen, D. C. E. Bortolotti, and J. L. Bohn, Phys. Rev. A {\bf 74}, 013623 (2006).} \footnotetext[2]{\hspace{2pt} S. Yi and H. Pu, Phys. Rev. A {\bf 73}, 061602(R) (2006).}