 0  0.2  0.4  0.6  0.8  1  0  50  100  150  200 Purity E$_{R}$t (a)  0  0.2  0.4  0.6  0.8  1  0  20  40  60  80  100 Purity E$_{R}$t (b) FIG. 8: Variation of the purity of the initial states | L 〉 (dashed line) and the Gaussian state | ψ$_{G}$ ( x ) 〉 (solid line) for the kick rates 100 Hz and (a) m = 10, (b) m = 100. The other parameters are the same as Fig. 2.  0  0.2  0.4  0.6  0.8  1  0  2  4  6  8  10 Purity E$_{R}$t (a)  0  0.2  0.4  0.6  0.8  1  0  2  4  6  8  10 Purity E$_{R}$t (b) FIG. 9: Variation of the purity of the initial states | L 〉 (dashed line) and the Gaussian state | ψ$_{G}$ ( x ) 〉 (solid line) for the kick rates 10 4 Hz and (a) m = 10, (b) m = 100. The other parameters are the same as Fig. 2. of the laser from the trapped atom, it is reasonable to consider a large value of m . Further, note that we are considering the decoherence in the external states of the atom (due to its trapping in a lattice), that occurs due to the decoherence in the internal states (electronic states) of the atom. We here focus on how to reduce the effect of this decoherence in the external state of the atom. We here analyze the time-evolution of the initial wave function from the first principle using the Schrodinger equation, not in the framework of master equation. In case of master equation, one takes average over the bath degrees of freedom and thus loses the essence of the physics that deals with random phase kick. Our numerical procedure comprises of the following steps: We calculate the wavefunction at each dt time- 9