Dynamical trapping and transmission of matter-wave solitons in a collisionally inhomogeneous environment

We investigate bright matter-wave solitons in the presence of a spatially varying scattering length. It is demonstrated that a soliton can be confined due to the inhomogeneous collisional interactions. Moreover, we observe the enhanced transmission of matter-wave solitons through potential barriers for suitably chosen spatial variations of the scattering length. The results indicate that the manipulation of atomic interactions can become a versatile tool to control matter-wave dynamics.

Figure 1

The spatial variation of the scattering length for $B=450+\epsilon x$ (G) and magnetic field gradients $\epsilon =0$ (dotted line), $\epsilon =5\mathrm{G}∕\mu \mathrm{m}$ (solid line) and $\epsilon =25\mathrm{G}∕\mu \mathrm{m}$ (dashed line).

Figure 2

(Color online) Spatiotemporal contour plot of the density of a bright matter-wave soliton for $B_0=450\mathrm{G}$ and magnetic field gradients $\epsilon =5\mathrm{G}∕\mu \mathrm{m}$ (top panel) and $\epsilon =25\mathrm{G}∕\mu \mathrm{m}$ (bottom panel). The dashed line in the left panel corresponds to the analytical prediction according to Eq. (5).

Figure 3

(Color online) Scattering of a soliton off a barrier. The left (right) vertical axis shows the soliton density ${\mid \psi \mid }^2$ (scattering length $a$). The incident soliton is shown at its initial location at $x=0$. The transmitted and reflected parts of the soliton are shown at $t=6\mathrm{ms}$ (inhomogeneous case); the former is located at $x\approx -31\mu \mathrm{m}$ and the latter at $x\approx -11\mu \mathrm{m}$. The barrier is located at $x_{\mathrm{B}}=-20\mu \mathrm{m}$ (shaded area). The spatial dependence of the scattering length $a\left(x\right)$, forming a dip at the location of the barrier, is also shown.

Figure 4

The transmission $T$ as a function of the inverse width $w$ of the inhomogeneity, in units of ${\xi }^{-1}$ (top panel), or the soliton’s incident velocity $k$, in units of $c$ (bottom panel). Dashed and solid lines correspond to the collisionally homogeneous and inhomogeneous cases, respectively.