0 0.5 1 1.5 2 2.5 3 time (sec) 0 0.2 0.4 0.6 0.8 1 Probability (a) 0 0.5 1 1.5 2 2.5 3 time (sec) 0 0.2 0.4 0.6 0.8 1 Probability (b) FIG. 3: Variation of the probability that the single wave packet remains in the initial left well (solid line) at x = 0 and in the right well (dotted line) with time for (a) Z$_{f}$ = 0 . 05 and (b) Z$_{f}$ = 0 . 1. The parameters are σ = 0 . 1 λ , V$_{xy}$ = 36 E$_{R}$ , δθ = π/ 2, δφ = 0, and E$_{R}$ = 3 . 5 kHz. overlap with the other eigenstates is negligible. This state is equivalent to a Gaussian wave packet ψ$_{G}$ ( x ) ≡ exp( − x $^{2}$/ 2 σ $^{2}$) which is peaked at the left well with center at x = 0. The width σ of this wave packet is much less than that of the left well. For the above set of values of { c$_{l}$ } , σ = 0 . 1 λ . We show in Fig. 3, the temporal behavior of the probability P$_{L}$ . Clearly, the wave packet tunnels, but never returns back to the initial left well completely. It slowly disperses over both the wells in the lattice. The figure for the probability in the initial left well is complemented using the figure for the probability in the corresponding right well. We next consider the effect of decoherence on the evolution of these initial atomic states in the double-well. The decoherence can occur due to spontaneous emission and the fluctuation of the intensity of the laser fields. In this paper, we focus on the case of spontaneous emission. The atom emits a photon of certain wavelength λ ′ while in the excited electronic states. This imparts a recoil momentum p ′ = ℏ c/λ ′ on the lattice [10], leading to an extra phase of the instantaneous wave function as follows: Due to the randomness of the spontaneous emission, the atom emits a photon at any random direction. Thus, ⃗ p ′ can be random and the time at which the phase kick occurs can also 6 ψ ( x, t ) → ψ ( x, t ) e − i ⃗ p ′ .⃗ r/ ℏ . (6) III. EFFECT OF DECOHERENCE