Rydberg Atoms In Magnetic Fields Research Articles

Non-Hydrogenic Rydberg Atoms in Magnetic Fields

The classical and quantal dynamics of non-hydrogenic Rydberg atoms in magnetic fields are investigated. Previous attempts to infer classical behaviour from quantum properties produced conflicting results: at low scaled energies (ε=−0.5) the nearest-neighbour statistics (NNS) were found to be at the chaotic (Wigner) limit while quantum phase-space distributions suggested a high degree of regularity. Here the classical limit is investigated directly by solving the equations of motion of the Diamagnetic Kepler problem (DKP) with an additional non-Coulombic model potential. It is found that typically trajectories are, over a long time-scale, ergodic. However over a shorter time-scale—in between collisions with the core—classical trajectories remain confined on the tori of the DKP. The origin of a well-known resonance in the NNS of hydrogen at ε= −0.316 is clarified by the comparison with the non-hydrogenic behaviour. However, the classical model only partially explains the quantum behaviour. The difficulties of quantizing such a system are discussed.

A Time-Dependent Approach to High-Resolution Photoabsorption Spectrum of Rydberg Atoms in Magnetic Fields

A robust time-dependent approach to the high-resolution photoabsorption spectrum of Rydberg atoms in magnetic fields is presented. Traditionally we have to numerically diagonalize a huge matrix to solve the eigen-problem and then to obtain the spectral information. This matrix operation requires high-speed computers with large memories. Alternatively we present a unitary but very easily parallelized time-evolution method in an inexpensive way, which is very accurate and stable even in long-time scale evolution. With this method, we perform the spectral calculation of hydrogen atom in magnetic field, which agrees well with the experimental observation. It can be extended to study the dynamics of Rydberg atoms in more complicated cases such as in combined electric and magnetic fields.

Spectral properties of a Rydberg atom immersed in a Bose-Einstein condensate

The electronic spectrum of a Rydberg atom immersed in a Bose-Einstein condensate is investigated. The Heisenberg equations of motions for the condensate and the Rydberg atom are derived. Neglecting the back action of the Rydberg atom onto the condensate decouples the equations describing the condensate and Rydberg atom. In this case the spectral structure of the Rydberg atom is completely determined by an effective potential which depends on the density distribution of the condensate. We study the spectral properties for the situation of an isotropic harmonic and anharmonic as well as axially symmetric confinement. In the latter case an intriguing analogy with Rydberg atoms in magnetic fields is encountered.

The diamagnetic Kepler problem

It has turned out that the analysis ofclassical periodic orbits is the key to understanding the modulations in thequantal spectra of hydrogen Rydberg atoms in magnetic fields. Inspired by this quantum chaological connection, we analyse some fundamental periodic orbits of the diamagnetic Kepler problem, abandoning the condition of vanishing azimuthal angular momentuml z used in the literature so far. We report the bifurcation and confluence schemes of the orbits in their dependence onl z and discuss the structural changes in terms of catastrophe theory.

Hydrogenic Rydberg atoms in strong magnetic fields: Theoretical and experimental spectra in the transition region from regularity to irregularity

For deuterium Rydberg atoms in a magnetic field of ∼6 T we compare the complete experimental spectrum in the range −190 cm−1 to −20 cm−1 with the positions and oscillator strengths of the corresponding quantum theoretically calculated photoabsorption lines. The agreement is excellent. The range of energy covered extends from the end of thel-mixing regime up to the regions where the approximate integrability of the problem is completely lost, and the corresponding classical system undergoes a transition to chaos.

Scaling Laws for Rydberg Atoms in Magnetic Fields

Empirical conjectures of Feneuille, based on new regularities observed in the quasi-Landau spectrum, are investigated. Scaling laws for Rydberg atoms in magnetic fields are obtained from Schr\"odinger's equation, in two different approximations. Our formulas support the empirical conjectures and show them to be closely connected with the dynamics of the electronic motion in the $z=0$ plane.