Figure 2

Transmission spectrum of a matter-wave cavity for a momentum eigenstate (solid blue) with kinetic energy \(\mathcal{E}\) and for a momentum distribution (dashed blue, \(\Delta z = {12}\) μm) as well as vanishing gravitational acceleration \(g = 0\). The peaks in the transmission spectrum give rise to resonances whose widths increase for larger kinetic energies. We scale the distance between two resonances by the cavity length (here \(d={15}\) μm) and the width of the individual resonances is related to the width of the barriers (here \(\sigma _{b} = {1}\) μm, \(V_{b}=1.42\times10^{-25}{\text{ J}}\)). The spectrum is obtained by the transfer matrix approach and discretizing the total transfer matrix into 10² sub-matrices