J Low Temp Phys (2010) 158: 58–64 DOI 10.1007/s10909-009-9925-8 Dynamical Instability of Coreless Vortices in F = 2 Spinor Bose-Einstein Condensates M. Takahashi · T. Mizushima · K. Machida Received: 16 June 2009 / Accepted: 22 July 2009 / Published online: 29 July 2009 © Springer Science+Business Media, LLC 2009 Abstract We theoretically investigate the low-lying excitation spectra of coreless vortex states in Bose-Einstein condensates (BECs) with F = 2 hyperfine spin degrees of freedom. Here, we extend the previous work in F = 1 spinor BEC. In addition to the dynamical instabilities in F = 1 coreless vortex states, we find an another set of dynamical instabilities due to different hyperfine spin interaction. The calculation is carried out in the possible parameter space of the F = 2 87 Rb atom. This study assists interpretation of experimental data and presents a general characteristics of the dynamical instability of F = 2 hyperfine spin system. whether the ground state of the spin interaction is in the cyclic or polar phase. Our study can encourages the experiments to examine our results. Keywords Bose-Einstein condensation · Quantum gases · Quantized vortices PACS 03.75.Mn · 03.75.Kk · 03.75.Lm · 67.30.he 1 Introduction Bose-Einstein condensates (BECs) with hyperfine spin F is called spinor BECs. The spinor BECs involve internal degrees of freedom and the order parameter is defined by a multicomponent vector. This system can be realized in a fully optical trap, where the spins are liberated and spin textures are allowed to be created. Due to the internal degrees of freedom, many kinds of non-trivial topological defects have been theo- retically proposed so far [1–5]. For instance, an interesting property of non-Abelian vortex states has been recently predicted [6]. In addition, an anisotropic long-range M. Takahashi ( ) · T. Mizushima · K. Machida Department of Physics, Okayama University, Okayama 700-8530, Japan e-mail: masahiro@mp.okayama-u.ac.jp