Figure 6

Influence of gravity on the resonances (a) and their widths (b) of a matter wave cavity (\(\sigma _{b} = {1}\) μm, \(V_{b}=1.42\times10^{-25}{\text{ J}}\) and \(d={15}\) μm). The plotted values correspond to the real and imaginary parts of the eigenvalues of the complex-scaled Hamiltonian, obtained by the Lagrange-mesh method. In addition to the resonances (solid lines), the eigenenergies of the triangular potential shown in Fig. 5(a) are included (dashed lines). If the gravitational acceleration is sufficiently strong, we expect that the right barrier becomes less important and bound states arise solely from the left barrier and the linear potential. As a consequence, the energies associated with the resonances approach the eigenenergies of the triangular potential (dashed lines). Moreover, for larger gravitational accelerations the resonances are closer to the continuum resulting in shorter lifetimes and subsequently larger widths of the resonances