Extracting Closed Classical Orbits from Quantum Recurrence Spectra of a Non-Hydrogenic Atom in Parallel Electric and Magnetic Fields

We show how to extract the closed orbits from the quantum spectra data. According to the closed orbit theory, each closed orbit produces a sharp peak in the recurrence spectra of a non-hydrogenic atom in parallel electric and magnetic fields. For a given initial state, closed-orbit theory gives the dependence of this recurrence amplitude on the initial angle of an orbit. By comparing the recurrence amplitude for different initial states, we can determine the initial angles of the closed classical orbits from the quantum recurrence spectra. Therefore, by integrating the Hamiltonian motion equations, we can obtain the closed orbits directly. This method can also be used to extract the closed orbits from the experimental data.