Figure 8

(a) Gaussian wave packet (\(\Delta z = {3}\) μm) prepared in the center of the gravitationally distorted matter-wave cavity (\(\sigma _{b} = {1}\) μm, \(V_{b}=1.42\times10^{-25}{\text{ J}}\), \(d={15}\) μm). A double Bragg pulse creates a superposition of the wave packet with opposite momenta \(\pm p_{0}\). Due to gravity, the transmission of the kicked wave packet through the left (blue region) and right barrier (red region) differs. The operators \(\hat{P}_{L}\) and \(\hat{P}_{R}\) project on the fraction of transmitted atoms through the left (blue shaded region) and right barrier (red shaded region) where the regions either end at \(z_{-}\) or start at \(z_{+}\). (b) Motion of the symmetrically kicked wave packet (initial width \(\Delta z = {3}\) μm, initial kick \(p_{0} = \pm 0.5 \times \sqrt{2 m V_{b}}\)) prepared in the center of the matter-wave cavity for different gravitational accelerations. After a short period of time both wave packets are delocalized over the whole cavity where the white lines represent the position of the barriers. The amplitude of the resulting oscillations decreases due to periodic outcoupling of the trapped atoms