Theoretical study on the stability of a vortex ring in an axisymmetrically and harmonically trapped dipolar dondensate

We theoretically study the stability of a vortex ring (VR) in an axisymmetrically and harmonically trapped dipolar condensate. Specifically, we focus on the case in which the dipoles are all aligned along the axial direction. Assuming a condensate of large size, we approach the problem by taking into account the velocity formula derived from the time-dependent Gross-Pitaevskii equation (GPE) by the method of matched asymptotic expansion in the Thomas-Fermi limit for the filament model of a circular VR subjected to bending-wave instability [1]. The stable region, where VR is robust against the linear instability of bending waves, is determined for wide ranges of scaled dipole strength and aspect ratio of the trapping potential. To visualize the locomotion and probe the dynamical aspect of VR traversing in a realistic dipolar BEC, we numerically solve the time-dependent GPE related to the recently demonstrated dysprosium BEC [2]. Furthermore, we address the effect of quantum fluctuation originating from Lee-Huang-Yang effect [3] in such dipolar BECs.

[1] T.-L. Horng et al., Phys. Rev. A 74, 041603 (2006).
[2] H. Kadau et al., Nature 500, 194 (2015).
[3] F. Wächtler and L. Santos, Phys. Rev. A 93, 061603 (2016), and H. Saito, J. Phys. Sco. Jpn. 85, 053001 (2016).