Manifestations of the Roton Mode in Dipolar Bose-Einstein Condensates

We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that 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 perturbation theory, we relate these oscillations to a previously identified “rotonlike” mode in dipolar BECs. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been predicted previously.

Figure 1

The red (thin) dotted line marks the maximum dipole strength, for a given trap aspect ratio $\lambda$, below which a rotationless ($k=0$) DBEC is dynamically stable. The colored regions represent the dynamically stable region for a $k=1$ DBEC, while the pink (darker) region is where radial oscillations with local minima are observed. The inset (a) is an isodensity surface plot of a $k=0$ DBEC perturbed by a small Gaussian potential centered on the trap axis, while the inset (b) is an isodensity surface plot of a $k=1$ DBEC. The presence of radial oscillations is clear in both cases.

Figure 2

Radial profiles of the $k=0$ DBEC subject to the perturbing potential $U^{\prime }(\mathbf{r})=\hslash {\omega }_{\rho }\exp [-{\rho }^2/2(0.2a_{\mathrm{ho}}{)}^2]$ in a trap with aspect ratio $\lambda =17$. The red dash-dotted line represents the trapping potential at $z=0$, the black solid line represents the radial profile of the DBEC at $D=100$, and the blue dotted line represents the radial profile at $D=181.2$, near the point of dynamic instability for the $k=0$ DBEC. The “+” signs represent the perturbation theory results and the thin dotted lines represent the unperturbed radial profiles at the corresponding dipole strengths.

Figure 3

Radial profiles of excitations on a rotationless DBEC with dipole strength $D=181.2$ in a trap with aspect ratio $\lambda =17$. The solid blue line represents the BdG roton mode while the red marks represent the $F$-operator eigenfunction with eigenvalue $\mu ,|{\phi }_0⟩$.