The eigenenergy $E_{n}$ has both linear and quadratic terms in the quantum number $n$. The time evolution of the CS generated by the PT Hamiltonian, $$\chi_{\beta}(x,t)=\sum_{n=0}^{\infty}d_{n}^{\beta}\psi_{n}(x)e^{-iE_nt}, \label{timeevolution}$$ is such that, at short times, the center of the wave-packet reproduces the classical motion, due to the linear term in $n$ in the energy eigenvalues. The quadratic term in $n$ is instead responsible for revival and fractional revivals [@averbukh; @robinett], taking place on a longer time scale. In fact, it is easy to check that after the revival time $T_{rev}=\pi/\alpha^2$ (or integer multiples of it), the initial coherent state localizes back to its form after spreading. Here however, we are interested in fractional revivals, which instead take place after a time interval $(r/s)T_{rev}$, with $r$ and $s$ mutually prime integers. At fractional revival times the initial wave-packet partially localizes into a superposition of spatially distributed sub-packets, each of which closely resembles the initial wave-packet: when $s$ is even, the wave-packet breaks into $s/2$ wave-packets, when instead $s$ is odd, the state is a superposition of $s$ distinct states. This means that one obtains a Schrödinger cat state, superposition of two CS with opposite phases, at one fourth of the revival time, while 