Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. I. Physical picture and calculations

Abstract

This is the first of two papers that develop the theory of oscillatory spectra. When an atom is placed in a magnetic field, and the absorption spectrum into states close to the ionization threshold is measured at finite resolution, so that individual energy levels are not resolved, it is found that the absorption as a function of energy is a superposition of sinusoidal oscillations. These papers present a quantitative theory of this phenomenon. In this first paper, we describe the physical ideas underlying the theory in the simplest possible way, and we present our first calculations based upon the theory. In the second paper, the theory is developed in full detail, proofs of all of the assertions are given, and we describe the algorithm that was used to make the calculations.

Closed-orbit theory for photodetachment in a time-dependent electric field

“…On the other hand, we noticed that some classical trajectories of the photoelectron can be driven back to the source region by a strong single-cycle THz pulse. These observations remind us of a general picture already recognized in the standard closed-orbit theory [3][4][5], which addresses the correspondence between the oscillatory photoionization (or photodetachemnt) rate and the possible closed classical orbits embedded in the system.…”

“…Following the general picture depicted by closed-orbit theory [3][4][5], an external field can modulate the photon absorption rate in the photoionization and photodetachment processes by driving back an outgoing electron wave to the source region where the initial bound state is localized. The returning electron wave interferes with the outgoing wave near the source center.…”

“…Its studies often promise an intuitive picture of the embedded dynamics, which not only reveals an interesting correspondence between classical and quantum mechanics, but also allows a better control and manipulation on a microscopic scale. The general physical picture and formalism are known as closed-orbit theory [3][4][5] which has been applied or extended in different situations. However, almost all the systems investigated before are time independent and therefore energy conserving [6][7][8][9][10][11][12][13][14][15].…”

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

“…Purely semiclassical calculations have also been undertaken, reaching an excellent agreement with experimental observations and exact quantum calculations. The semiclassical formalism, known as 'Closed orbit theory' [13], starts from the semiclassical propagator (1) and explains the recurrences observed with classical periodicity by the propagation of the laser excited electron waves along the classical trajectories that start and end at the nucleus: every such orbit produces a peak whose height depends on the classical amplitude of the orbit. If several orbits have the same or nearly the same period (as happens in Fig 1) the height of the peak depends on the interference between the orbits, and the phases φ k of Eq.…”

Closed orbits and their bifurcations in the crossed-field hydrogen atom

“…Closed-orbit theory [1,2] has proven to be the key tool to analyze the photoabsorption spectra of atoms in external fields. It interprets spectral oscillations semiclassically in terms of closed orbits of the underlying classical system, i.e.…”