Phonon Instability with Respect to Soliton Formation in Two-Dimensional Dipolar Bose-Einstein Condensates

The partially attractive character of the dipole-dipole interaction leads to phonon instability in dipolar Bose-Einstein condensates, which is followed by collapse in 3D geometries. We show that in 2D, the nature of the post-instability dynamics is fundamentally different, due to the stabilization of 2D solitons. As a result, a transient gas of attractive solitons is formed, and collapse may be avoided. In the presence of an harmonic trap, the post-instability dynamics is characterized by a transient pattern formation followed by the creation of stable 2D solitons. This dynamics should be observable in ongoing experiments, allowing for the creation of stable 2D solitons for the first time ever in quantum gases.

Figure 1

The 2D soliton gas after phonon instability of an homogeneous dipolar BEC. For both the figures, $\mu =-0.2$ and $g/(\sqrt{2\pi }{l}_z)=10$. (top) $\perp$-configuration, $\beta =-0.2$, $t=484/{\omega }_z$; (bottom) $||$-configuration, $\beta =0.3$, and $t=108/{\omega }_z$.

Figure 2

Stability diagram of an anisotropic soliton as a function of $\beta$ and ${\tilde{g}}_{\mathrm{cr}}=g{N}_{\mathrm{cr}}/\sqrt{2\pi }{l}_z$, where for $N>N_{\mathrm{cr}}$, the soliton is unstable against collapse even for $\beta >3/4\pi$.

Figure 3

Trapped BEC in the $\perp$-configuration. In the simulations, ${\omega }_{\rho }=0.001{\omega }_z$, $g/(\sqrt{2\pi }{l}_z)=200$, and $\beta =0.3$ ($t<0$) and $-0.3$ ($t>0$). (left) Formation of ring structures ($t=810/{\omega }_z$); (right) Final soliton at the trap center ($t=7500/{\omega }_z$).

Figure 4

Trapped BEC after tilting at $t=0$ from $\perp$ to $||$ configuration, with ${\omega }_{\rho }=0.001{\omega }_z$, $g/(\sqrt{2\pi }{l}_z)=200$, and $\beta =0.3$. (left) Anisotropic ring formation ($t=1092/{\omega }_z$); (right) Final formation of an anisotropic soliton ($t=1281/{\omega }_z$).