Figure 9

Asymmetric transmission (a) and relative uncertainty (b) of a wave packet starting 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). The wave packet (initial width \(\Delta z = {3}\) μm) experiences a double Bragg pulse, resulting in a superposition of two wave packets with opposite momenta \(\pm p_{0}\) and kinetic energies \(\mathcal{E} = p_{0}^{2} / (2 m)\). The asymmetric transmission corresponds to the difference between the transmission through the left and right barrier of the matter-wave cavity. (a) No resonances are observed in the asymmetric transmission because of the large initial momentum width of the (localized) wave packet. (b) The relative uncertainty associated with the asymmetric transmission contains a local maximum for small momentum kicks and shows the best sensitivity for the largest initial momentum and largest acceleration. While \(\delta g_{-}\) denotes the relative uncertainty for an experiment with N particles and ν repetitions, we plot the quantity \(\sqrt{N}\sqrt{\nu}\delta g_{-}\) which is the single-particle uncertainty without repetitions, assuming shot-noise limited measurements with non-interacting particles