Dynamically stable multiply quantized vortices in dilute Bose-Einstein condensates

Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.

Figure 1

Grayscale plot of the maximum imaginary part of the Bogoliubov eigenvalues as a function of the interaction strength $\tilde{g}=4\pi aN∕a_r$ and inverse trap anisotropy $1∕\lambda ={\omega }_r∕{\omega }_z$ for the two-quantum vortex state. White denotes the dynamically stable regions with vanishing imaginary parts, and black corresponds to maximum imaginary part $0.185{\omega }_r$, the scale in between being linear. The striplike instability regions for small $1∕\lambda$ are in fact continuous, although they seem fragmentary due to discretization of the parameter space in the computations.

Figure 2

Maximum imaginary part of the Bogoliubov eigenvalues for the two-quantum vortex state as a function of the interaction strength $\tilde{g}=4\pi aN∕a_r$ for the spherically symmetric trap geometry with $\lambda =1$.

Figure 3

Maximum imaginary part of the Bogoliubov eigenvalues as a function of the interaction strength $\tilde{g}=4\pi aN∕a_r$ and inverse trap anisotropy $1∕\lambda$ for the three-quantum vortex state. In the grayscale white corresponds to dynamically stable state and black the imaginary part value $0.208{\omega }_r$ of the frequency. The large instability regions are due to modes with ${\kappa }_q=2$, and the thin lines in between them are caused by modes with ${\kappa }_q=3$.

Figure 4

Maximum imaginary part of the Bogoliubov eigenvalues for the three-quantum vortex state as a function of the interaction strength $\tilde{g}=4\pi aN∕a_r$ in the spherically symmetric trap geometry.

Figure 5

Maximum imaginary part of the Bogoliubov eigenvalues as a function of the interaction strength $\tilde{g}=4\pi aN∕a_r$ and inverse trap anisotropy $1∕\lambda$ for the four-quantum vortex state. Complex frequencies exist in this case for excitation quantum numbers ${\kappa }_q=2$, 3, 4, and 5. In the linear grayscale black corresponds to imaginary part value $0.231{\omega }_r$ of the frequency and white to zero.

Figure 6

Maximum imaginary part of the Bogoliubov eigenvalues for the four-quantum vortex state as a function of the interaction strength $\tilde{g}=4\pi aN∕a_r$ in the spherically symmetric trap geometry.