Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate

We demonstrate that a matter-wave bright soliton can be stabilized in 2D free space by causing the strength of interactions to oscillate rapidly between repulsive and attractive by using, e.g., Feshbach resonance.

Figure 1

Time evolution of the peak density $|\psi (r=0){|}^2$ and the monopole moment $⟨r⟩=\int r|\psi {|}^{2}d\mathbf{r}$. The interaction $g(t)=-2\pi +8\pi \sin \Omega t$ is switched on and simultaneously the radial confinement potential is switched off from $t=0$ to 20 according to Eq. (4), where $\Omega =40$ in (a) and $\Omega =30$ in (b). The plots oscillate rapidly at $\Omega$ (which is beyond the resolution limit of the graph), and the vertical width of the plots represents the amplitude of the rapid oscillations. The insets show the density profiles $|\psi (r){|}^2$ at $t=50$ (solid curves) and $t=0$ (dashed curves).

Figure 2

(a) $(g_1/\Omega {)}^{1/2}$ dependence of the monopole moment $⟨r⟩$ and (b) $\Omega /g_1$ dependence of the breathing-mode frequency ${\omega }_{\mathrm{b}\mathrm{r}}$, where $g_0=-2\pi$. The circles are obtained by varying $g_1$ for $\Omega =30$, and the squares by varying $\Omega$ for $g_1=8\pi$. The dashed lines show $1.06(g_1/\Omega {)}^{1/2}$ in (a) and $0.32\Omega /g_1$ in (b), which are determined to best fit the plots.