an effective classical particle whose coordinate is $z$, moving in a potential $V$ with the initial energy $E_{eff}^{0}=[%
\stackrel{.}{z}(t)|_{t=t_{0}}]^{2}/2+V|_{t=t_{0}}$. If the trapping potential is time-independent, the effective potential $V$ is time-independent too, and the motion of the effective particle is regular; otherwise, for the time-dependent trapping potential, $V$ varies with time and the corresponding motion is anharmonic and even chaotic. The chaotic dynamics in atomic tunneling will be detailed in the following sections. For the time-independent constant coupling $K$ , the Hamiltonian of the effective particle is given by $$\begin{aligned}
H_{eff} &=&\frac{1}{2}p_{z}^{2}+V=\frac{1}{2}(1-H^{2})  \nonumber \\
V &=&\frac{1}{2}z^{2}(1-\Lambda H+\frac{1}{4}\Lambda ^{2}z^{2})+(\frac{1}{2}%
\Delta E\Lambda z^{3}+\frac{1}{2}\Delta E^{2}z^{2}-\Delta EHz).\end{aligned}$$ The Hamiltonian’s canonical equations of the motion are $$\frac{dz}{dt}=\frac{\partial H_{eff}}{\partial p_{z}} 
\begin{array}{lll}
& , & 
\end{array}
\frac{dp_{z}}{dt}=-\frac{\partial H_{eff}}{\partial z}.$$ For the symmetric trapping potential $(\Delta E=0)$, the effective potential $V$ is time-independent, increasing the value of $(1-\Lambda H)$ from negative to positive changes the effective potential from a double-well to a parabolic. The effective particle moves between the classical turning points, where the kinetic energy of the effective particle is zero. Fig. 1 shows the changing of the shape of the effective potential, $(A)$ for different values of $H$ with fixed value of $\Lambda $, and $(B)$ 