Figure 7

(a) Transmission of a wave packet (initial width \(\Delta z = {12}\) μm) with initial momentum \(p_{0}\) scattered from the matter-wave cavity (\(\sigma _{b} = {1}\) μm, \(V_{b}=1.42\times10^{-25}{\text{ J}}\), \(d={15}\) μm). To take into account the influence of the gravitational field g prior to scattering, we use the kinetic energy \(\mathcal{E} = \mathcal{E}_{0} - m g |z_{0}|\) as reference where \(\mathcal{E}_{0}\) describes the initial kinetic energy and \(z_{0}\) the initial position of the wave packet. Without considering the self-interaction of the atomic cloud, the resonances wash out for \(g > 0\) (\(g = {1.3}\text{ mm/s}^{2}\)) and become more prominent for \(g < 0\) (\(g = {-0.8}\text{ mm/s}^{2}\)). A repulsive self-interaction \(\gamma > 0\) (here \(\gamma = 3.51\times10^{-38}\text{ m}\), \(g = {0}\text{ mm/s}^{2}\)) leads to a suppression of the resonances (dashed line). (b) Momentum width of the time-evolved wave packet. The individual plots end at the time of the turning point of a classical particle with same momentum \(\mathcal{E}/V_{b}=0.77 \). The momentum width Δp is scaled by \(p_{L} = m v_{R}\) with the recoil velocity \(v_{R} = {5.8845}\text{ mm/s}\) of the ⁸⁷Rb \(\mathrm{D_{2}}\)-transition. The slope of the barriers is affected by gravity and in turn deforms the wave packet upon propagation. The effect of the direction of gravity is shown in the insets to the right. As a consequence, the wave packet contracts in momentum for \(g < 0\), while the width is increased for \(g > 0\)