Low-lying excitations of vortex lattices in condensates with anisotropic dipole-dipole interaction

We investigated the low-lying collective excitations of quasi-two-dimensional dipolar Bose-Einstein condensates confined in a rotating harmonic potential using the Bogoliubov–de Gennes equation. By varying the trap rotation frequency and dipolar interaction strength, we show how the anisotropic dipole-dipole interaction modifies the collective excitations of the condensates. In particular, under strong dipolar interaction, the vortex-displacement excitations differ significantly from the nondipolar case.

Figure 1

Frequencies of the low-lying excitations versus the dipolar interaction strength for rotation frequency $\mathrm{\Omega }=0.3$. From left to right, the insets show the density profiles of the ground states corresponding to $g_d/g_0=0.02$, 0.12, and 0.16, respectively.

Figure 2

Density profiles of the ground states with $\mathrm{\Omega }=0.5$ and for various DDI strengths. From (a) to (g), the relative dipolar interaction strengths are $g_d/g_0=0.005$, 0.055, 0.085, 0.12, 0.135, 0.15, and 0.175, respectively.

Figure 3

Excitation frequencies of the VDMs as functions of the DDI strength. From left to right, distinct shaded regions correspond to ground states with 8, 7, 6, 5, 4, 3, and 2 vortices. T, C, Q, and R label the Tkachenko, common, quadratic, and rational modes, respectively. O denotes modes that do not fall into these four types. For the 7-, 3-, and 2-vortex states, movies of $n_p(\mathbf{\rho },t)$ perturbed by different modes are shown in the Supplemental Material [46].

Figure 4

Density profiles of the ground states under the DDI strength $g_d/g_0=0.15$ for $\mathrm{\Omega }=0.7$ (a) and 0.9 (b).

Figure 5

Snapshots of the density profiles $n_p(\mathbf{\rho },t)$ [Eq. (14)] perturbed by different excitation modes. Other parameters are $g_d/g_0=0.15$ and $\mathrm{\Omega }=0.7$.

Figure 6

Excitation mode functions $|u_j{\left(\mathbf{\rho }\right)|}^2$ (left panels) and $|v_j{\left(\mathbf{\rho }\right)|}^2$ (right panels) for $j=7$ (upper panels) and 17 (lower panels). Other parameters are $g_d/g_0=0.15$ and $\mathrm{\Omega }=0.7$.