Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

We present a family of exact solutions of the one-dimensional nonlinear Schrödinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.

Figure 1

The dynamics of the Feshbach resonance managed soliton in the expulsive parabolic potential given by Eq. (8). The parameters are given as follows: $\lambda =2\times {10}^{-2}$, $g_0=0.25$, $A_c=1$, $A_s=2.4$, and $k_0=0.03$.

Figure 2

Time-periodic atomic exchange between the bright soliton and the background given by Eq. (13). The range of time is (a),(b) $t=[0,5]$ and (c) $t=[20,25]$. The parameters are given as follows: $\lambda =0.02$, $g_0=1$, $A_s=4.8$, (a) $A_c=0$, and (b),(c) $A_c=2.3$.