$\exp(\lambda \; K_{+} -\lambda^{*} \; K_{-})$ on the CS of Eq. \[timeevolution\], where $\lambda$ is the displacement parameter and $K_{+}$,$K_{-}$ are the SU(1,1) generators [@utpal]. The overlap between the initial and final states in terms of the Wigner distribution is $$|\langle\chi_{\beta}^{\mathrm{CS}}|\chi_{\beta^{'}}^{\mathrm{DCS}}\rangle|^2=\int\!\!\!\int W_{\mathrm{CS}}(x,p) W_{\mathrm{DCS}}(x,p)
dx\;dp,\label{wigoverlap1}$$ where $\chi_{\beta}^{\mathrm{CS}}$ is the initial CS evolved at time $t$ and $\chi_{\beta^{'}}^{\mathrm{DCS}}$ is the displaced coherent state (DCS) at the same time. After a long calculation we find the DCS and the above mentioned overlap can be written as $$\langle\chi_{\beta}^{\mathrm{CS}}|\chi_{\beta^{'}}^{\mathrm{DCS}}\rangle
=\sum_{n,m,p}\textbf{D}_{m,n,p}^{\;\beta,\beta^{'}}\;\;e^{-i(E_n-E_{n-m+p})t},\label{overlap}$$

where $$\begin{aligned}
\textbf{D}_{m,n,p}^{\;\beta,\beta^{'}}&=&\frac{\beta^{2n-m+p}(-\beta^{'})^{m}(\beta^{'})^{p}}{m!p!}
\times
\frac{\Gamma(2\rho+2n-m+p)\Gamma(\rho+n+\frac{1}{2})\Gamma(2\rho-m+p+1)\Gamma(\rho+n-m+p+
\frac{1}{2})}{\Gamma(n-m+1)\Gamma(\rho+n-m+\frac{1}{2})\Gamma(2\rho+p+1)\Gamma(2\rho+2n-2m+p)}\nonumber\\
&& \times
\frac{\Gamma(\rho+n-m+p+\frac{1}{2})}{\Gamma(2\rho+n-m+p)(n-m+p+\rho)}\;\;
e^{\eta(n-m+\rho/2+1/4)}.\end{aligned}$$

Here $\lambda\!\!=\!|\lambda|e^{i\theta}$, $\beta^{'}\!\!\!=\!\tanh|\lambda|e^{i\theta}$ and $\eta=-2\log_e
(\cosh|\lambda|)$, after using the normal form of the disentanglement formula for SU(1,1) algebra [@perelomov]. We choose a symmetric potential for $\rho=50$, $\alpha=2\;a.u.$ and an initial CS parameter $\beta=0.4$. We have plotted the overlap of Eq. \[overlap\] at time $T_{rev}/8$ (Fig. \[plot\]) versus the displacement parameter $\lambda$. One has damped oscillations which are again caused by the interference pattern of the compass-like state. The two states becomes quickly orthogonal, showing the sensitivity of the state to displacement. This oscillation is similar to the one shown by the overlap between the displaced and the undisplaced compass-like state of the harmonic oscillator (HO) 