Fully Three Dimensional Breather Solitons Can Be Created Using Feshbach Resonances

We investigate the stability properties of breather solitons in a three-dimensional Bose-Einstein condensate with Feshbach resonance management of the scattering length and confined only by a one-dimensional optical lattice. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi-two-dimensional treatment. For moderate confinement we discover a new island of stability in the 3D case, not present in the quasi-2D treatment. Stable solutions from this region have nontrivial dynamics in the lattice direction; hence, they describe fully 3D breather solitons. We demonstrate these solutions in direct numerical simulations and outline a possible way of creating robust 3D solitons in experiments in a Bose-Einstein condensate in a one-dimensional lattice. We point out other possible applications.

Figure 1

The time dependence of the nonlinear coefficient, $g$, switching-off function, $f(t)$, and optical-lattice strength, $\epsilon$, in the numerical experiment which leads to the establishment of stable 3D breathing solitons supported by the combination of the quasi-1D lattice and FRM. The shaded area indicates rapid oscillations of $g(t)$, which account for the FRM.

Figure 2

Evolution of the amplitude of the central peak in the pattern comprising five cells of the optical lattice (shown in the inset). The normalized parameters are $g_{0\mathrm{f}}=-30$, $g_{1\mathrm{f}}=4g_{0\mathrm{f}}$, ${\epsilon }_{\mathrm{f}}=20.5$, $\Omega =22$, ${\omega }_{\perp }=0.3$, $t_1=30$, $t_2=100$, $t_3=120$, and $t_4=130$. The snapshots in the inset is taken at $t=6000$. The unit of time is $m{\lambda }^2/({\pi }^2\hslash )$.

Figure 3

Stability regions for the 3D solitons in the $(|g_{0\mathrm{f}}|,\Omega )$ plane, as predicted by the variational approximation (shaded area), and found from direct simulations of the Gross-Pitaevskii equation (circles). Other parameters are as in Fig. 2, except ${\epsilon }_{\mathrm{f}}=50$. Note the similarity of the lower region to that of Fig. 4. This region corresponds to Q2D solitons. On the other hand, the upper region contains fully 3D solitons. The borders of the VA stability regions were found analytically and will be given in a fuller version [15]. The lowest excitation frequency of the confining potential is ${\Omega }_0=26.76$.

Figure 4

Same as Fig. 3, but for Q2D treatment.