Quasi-Landau resonances in the spectra of rubidium Rydberg atoms in crossed electric and magnetic fields

A doubly anharmonic oscillator in an induced electric dipole system

The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is that it gives rise to an analogue of a spinless particle subject to the doubly anharmonic oscillator. Then, it is shown that analytical solutions to the Schrödinger equation can be obtained. Another point raised is that the quantum effects on the induced electric dipole moment can be observed if the uniform magnetic field possesses a discrete set of values.

Some aspects of an induced electric dipole moment in rotating and non-rotating frames

Quantum effects on a neutral particle (atom or molecule) with an induced electric dipole moment are investigated when it is subject to the Kratzer potential and a scalar potential proportional to the radial distance. In addition, this neutral is placed in a region with electric and magnetic fields. This system is analysed in both non-rotating and rotating reference frames. Then, it is shown that bound state solutions to the Schrödinger equation can be achieved and, in the search for polynomial solutions to the radial wave function, a restriction on the values of the cyclotron frequency is analysed in both reference frames.

Effects on a Landau-type system for a neutral particle with no permanent electric dipole moment subject to the Kratzer potential in a rotating frame

The behaviour of a neutral particle (atom, molecule) with an induced electric dipole moment in a region with a uniform effective magnetic field under the influence of the Kratzer potential (Kratzer 1920 Z. Phys.3, 289-307. (doi:10.1007/BF01327754)), and rotating effects is analysed. It is shown that the degeneracy of the Landau-type levels is broken and the angular frequency of the system acquires a new contribution that stems from the rotation effects. Moreover, in the search for bound state solutions, it is shown that the possible values of this angular frequency of the system are determined by the quantum numbers associated with the radial modes and the angular momentum, the angular velocity of the rotating frame and by the parameters associated with the Kratzer potential.

Classical dynamics and localization of resonances in the high-energy region of the hydrogen atom in crossed fields

When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom, a saddle point (called the Stark saddle point) appears. For energies slightly above the saddle point energy, one can find classical orbits that are located in the vicinity of this point. We follow those so-called quasi-Penning orbits to high energies and field strengths, observing structural changes and uncovering their bifurcation behavior. By plotting the stability behavior of those orbits against energy and field strength, the appearance of a stability apex is reported. A cusp bifurcation, located in the vicinity of the apex, will be investigated in detail. In this cusp bifurcation, another orbit of similar shape is found. This orbit becomes completely stable in the observed region of positive energy, i.e., in a region of parameter space, where the Kepler-like orbits located around the nucleus are already unstable. By quantum mechanically exact calculations, we prove the existence of signatures in quantum spectra belonging to those orbits. Husimi distributions are used to compare quantum-Poincaré sections with the extension of the classical torus structure around the orbits. Since periodic orbit theory predicts that each classical periodic orbit contributes an oscillating term to photoabsorption spectra, we finally give an estimation for future experiments, which could verify the existence of the stable orbits.

Extracting multidimensional phase space topology from periodic orbits

We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our findings for the hydrogen atom in crossed electric and magnetic fields.

Hydrogen atom in the presence of uniform magnetic and quadrupolar electric fields: integrability, bifurcations, and chaotic behavior

We investigate the classical dynamics of a hydrogen atom in the presence of uniform magnetic and quadrupolar electric fields. After some reductions, the system is described by a two degree of freedom Hamiltonian depending on two parameters. On the one hand, it depends on the z component of the canonical angular momentum P(phi), which is an integral because the system is axially symmetric; and on the other it also depends on a parameter representing the relative field strengths. We note that this Hamiltonian is closely related to the one describing the generalized van der Waals interaction. We report three cases of integrability. The structure and evolution of the phase space are explored intensively by means of Poincaré surfaces of section when the parameters vary. In this sense, we find several bifurcations that strongly change the phase space structure. The chaotic behavior of the system is studied and three order-chaos transitions are found when the system passes through the integrable cases. Finally, the ionization mechanics is studied.