Figure 5

(a) Resonances and bound states of the distorted matter-wave cavity (top) and a triangular potential (bottom). The resonances (green solid lines) of the matter-wave cavity (green) are modeled by quasi-bound states whose lifetime correspond to the width (shaded line) of the respective resonance. In contrast, the asymptotic of the triangular potential (orange) allows bound states (orange solid lines). To compare both cases, the left boundary of the triangular potential (orange) is chosen such that it correspond to the center of the left barrier of the matter-wave cavity (green). For a strong acceleration, we expect the lower resonances of the matter-wave cavity to approach the eigenenergies of the triangular potential. (b) Comparison between the transmission spectrum (red solid line) from Fig. 2 and Lorentzian profiles (blue solid lines), defined in Eq. (9), associated with the individual resonances for \(g=0\). The eigenenergies and widths are obtained by a Lagrange-mesh method which diagonalizes the Hamiltonian that describes the matter-wave cavity (\(\sigma _{b} = {1}\) μm, \(V_{b}=1.42\times10^{-25}{\text{ J}}\), and \(d={15}\) μm). The Lorentzian profiles show good agreement with the transmission spectrum while the overlap between resonances is negligible