Bright Soliton Trains of Trapped Bose-Einstein Condensates

We variationally determine the dynamics of bright soliton trains composed of harmonically trapped Bose-Einstein condensates with attractive interatomic interactions. In particular, we obtain the interaction potential between two solitons. We also discuss the formation of soliton trains due to the quantum mechanical phase fluctuations of a one-dimensional condensate.

Figure 1

The relative motion of two solitons. There are 5000 atoms in each soliton and $a=-3a_0$, with $a_0$ the Bohr radius. The solid curve is the solution of the exact equation of motion for $\eta (t)$. The dashed curve is the solution of Eq. (9) with $V(\eta )=({\eta }^2/2q_z^4)\exp (-{\eta }^2/4q_z^2)$. The points are experimental data obtained using the same apparatus described in Ref. 14. In the experiment more than two solitons were created. We focused on two large and adjacent ones.

Figure 2

Soliton train formation. The solid curve is the density and the dashed curve is the phase of the condensate. Initially, we start with an equilibrium condensate profile for ${10}^4$ atoms with a scattering length of $200a_0$. The scattering length is then instantaneously changed to $a=-3a_0$. The trap parameters are obtained from Strecker et al. [14].