Stability of Dark Solitons in Three Dimensional Dipolar Bose-Einstein Condensates

The dynamical stability of dark solitons in dipolar Bose-Einstein condensates is studied. For standard short-range interacting condensates, dark solitons are unstable against transverse excitations in two and three dimensions. On the contrary, due to its nonlocal character, the dipolar interaction allows for stable 3D stationary dark solitons, opening a qualitatively novel scenario in nonlinear atom optics. We discuss in detail the conditions to achieve this stability, which demand the use of an additional optical lattice, and the stability regimes.

Figure 1

Density plot of the Snake Instability: The Dark Soliton at $t=0$ starts to oscillate and eventually breaks.

Figure 2

Numerical results for the imaginary part of the excitation energies of a DS for $m/m^{*}=1$, and $\beta =0$ (triangles), $-0.5$ (squares), and 1 (circles). Solid lines correspond to the analytical result for low momenta.

Figure 3

Numerical results for the imaginary part of the excitation energies of a DS for $\beta =0$, and $m/m^{*}=0.2$ (squares), 0.1 (triangles), and 0.05 (circles). Solid lines correspond to the analytical result for low momenta.

Figure 4

Real part of the excitation energies of a DS for $m/m^{*}=0.1$ and $\beta =1.6$. Solid line corresponds to the analytical result for low momenta while empty circles correspond to numerical results.