Roton-Maxon Spectrum and Stability of Trapped Dipolar Bose-Einstein Condensates

We find that pancake dipolar condensates can exhibit a roton-maxon character of the excitation spectrum, so far observed only in superfluid helium. We also obtain a condition for the dynamical stability of these condensates. The spectrum and the border of instability are tunable by varying the particle density and/or the confining potential. This opens wide possibilities for manipulating the superfluid properties of dipolar condensates.

Figure 1

Dispersion law ${ϵ}_0(q)$ for (a) $\beta =1/2$, $\mu /\hslash \omega =343$; (b) $\beta =0.53$, $\mu /\hslash \omega =46$ (upper curve) and $\beta =0.47$, $\mu /\hslash \omega =54$ (lower curve). The solid curves show the numerical results, and the dotted curves the result of Eq. (9).

Figure 2

Critical values of $\beta$ for the rotonization (filled squares) and for the instability (hollow squares) versus $\mu /\hslash \omega$.