interval. (i) We evolve the wave function for a time δt ( ≤ dt ) if there occurs a phase kick at random time δt . (ii) Next we incorporate a random phase on the instantaneous wave function at the time δt , according to Eq.(6). (iii) The wave function again evolves for the time-interval dt − δt . If multiple phase kicks occur in a given interval dt , we evolve the wave function under the action of the Hamiltonian H during the time-intervals between two random kicks. (iv) We find the wavefunction at dt time-interval. We use a Monte Carlo method over N = 50 iterations. Thus at any time t , the density matrix of the atoms can be written as ρ ( x, x ′ ; t ) = (1 /N ) ∑ N k $_{=1}$ρ$_{k}$ ( x, x ′ ; t ), where ρ$_{k}$ ( x, x ′ ; t ) = ψ$_{k}$ ( x, t ) ψ ∗ $_{k}$( x ′ , t ) and ψ$_{k}$ ( x, t ) is the instantaneous wave function of the atom for the k th iteration. The expression for the probability P$_{L}$ ( t ) in the initial left well can then be written as Eq. (5). In the following, we also investigate the variation of the survival probability as given by and the variation of the purity of the wave function as given by We first investigate the evolution of the state | L 〉 which is a superposition of the two lowest-eigenenergy zero-quasi-momentum states | 0 〉 and | 1 〉 . For a small rate of random phase kicks (= 1 Hz or 10 Hz), the atoms tunnel back forth between the left and the right well. This means that the state remains almost coherent. This is true for both strong ( m = 100) and weak kicks ( m = 10). However for a larger kick rate ( ∼ 100 Hz), the larger the kick strength m , the more the wavefunction gets diffused throughout the double-well. One can see from Fig. 4 that the probability P$_{L}$ that the wavefunction remains in the initial left well becomes ∼ 0 . 5 at longer times. This is a signature of the decoherence. We have also plotted the survival probability F ( t ) of the initial wave function to see the nature of decoherence. In Fig. 5, we show how F ( t ) decays very rapidly with times if one increases the kick strength as well as the kick rate. The similar nature of the variation of probability being in the initial wells and the survival probability reflects the fact the decoherence occurs more due to population redistribution among the wells, rather than any dephasing. 10 A. Case of the state | L 〉 F ( t ) = ∫ dx ∫ dx $^{′}$ψ ( x, t = 0) ρ ( x, x $^{′}$; t ) ψ $^{∗}$( x $^{′}$, t = 0) , (7) M ( t ) = ∫ dx ∫ dx $^{′}$ρ ( x, x $^{′}$; t ) ρ ( x $^{′}$, x ; t ) . (8)