FIG. 4: Temporal variation of the probability that the wave function | L 〉 remains in the initial left well for (a) kick strength m = 10: kick rates 10 Hz (thick solid line), 100 Hz (dashed line), and 10 4 Hz (thin solid line), (b) kick strength m = 100: kick rates 1 Hz (thick solid line), 100 Hz (dashed line), and 10 4 Hz (thin solid line). We chose Z$_{f}$ = 0 . 1. The other parameters are the same as in Fig. 2. FIG. 5: temporal variation of the survival probability of the wave function | L 〉 for (a) kick strength m = 10: kick rates 10 Hz (thick solid line), 100 Hz (dashed line), and 10 4 Hz (thin solid line), (b) kick strength m = 100: kick rates 1 Hz (thick solid line), 100 Hz (dashed line), and 10 4 Hz (thin solid line). The other parameters are the same as in Fig. 4. be random. Further, because we consider an one-dimensional optical lattice in x direction, we consider the components of the recoil momentum only at x direction. Thus in spherical coordinate, the random phase can be written as exp[ − ik ′ x sin( θ ) cos( φ )], where k ′ = 2 π/λ ′ , and θ and φ represent the random direction of the outgoing photon. We write λ ′ = λ/m , where m defines the strength of the phase kick. Because, the wavelength of the standing wave in an optical lattice has to be much larger than the atomic wavelength and the detuning 7