Joerg Main

Exceptional points in atomic spectra

We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by exploiting characteristic properties of the degeneracies, which are branch point singularities. A possibility for the observation of exceptional points in an experiment with atoms is proposed.

Exceptional points in the spectra of atoms in external fields

Institut fu¨r Theoretische Physik 1, Universit¨at Stuttgart, 70550 Stuttgart, Germany(Dated: February 27, 2009)We investigate exceptional points, which are branch point singularities of two resonance eigen-states, in spectra of the hydrogen atom in crossed external electric and magnetic fields. A procedureto systematically search for exceptional points is presented, and their existence is proven. The prop-erties of the branch point singularities are discussed with effective low-dimensional matrix models,their relation with avoided level crossings is analyzed, and their influence on dipole matrix elementsand the photoionization cross section is investigated. Furthermore, the rare case of a connectionbetween three resonances almost forming a triple-degeneracy in the form of a cubic root branchpoint is discussed.

Spectral singularities in

We consider the model of a -symmetric Bose?Einstein condensate in a delta-function double-well potential. We demonstrate that analytic continuation of the primarily non-analytic term |?|2??occurring in the underlying Gross?Pitaevskii equation?yields new branch points where three levels coalesce. We show numerically that the new branch points exhibit the behaviour of exceptional points of second and third order. A matrix model which confirms the numerical findings in analytic terms is given.

{\mathcal P}{\mathcal T}

The variational method of coupled Gaussian functions is applied to Bose-Einstein condensates with long-range interactions. The time dependence of the condensate is described by dynamical equations for the variational parameters. We present the method and analytically derive the dynamical equations from the time-dependent Gross-Pitaevskii equation. The stability of the solutions is investigated using methods of nonlinear dynamics. The concept presented in this article will be applied to Bose-Einstein condensates with monopolar 1/r and dipolar 1/r{sup 3} interaction in the subsequent article [S. Rau et al., Phys. Rev. A 82, 023611 (2010)], where we will present a wealth of phenomena obtained using the ansatz with coupled Gaussian functions.

-symmetric Bose?Einstein condensates

We present variational calculations using a Gaussian trial function to calculate the ground state of the Gross-Pitaevskii equation (GPE) and to describe the dynamics of the quasi-two-dimensional solitons in dipolar Bose-Einstein condensates (BECs). Furthermore, we extend the ansatz to a linear superposition of Gaussians, improving the results for the ground state to exact agreement with numerical grid calculations using imaginary time and the split-operator method. We are able to give boundaries for the scattering length at which stable solitons may be observed in an experiment. By dynamic calculations with coupled Gaussians, we are able to describe the rather complex behavior of the thermally excited solitons. The discovery of dynamically stabilized solitons indicates the existence of such BECs at experimentally accessible temperatures.

Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept

We discuss the statistical properties of lifetimes of electromagnetic quasibound states in dielectric microresonators with fully chaotic ray dynamics. Using the example of a resonator of stadium geometry, we find that a recently proposed random-matrix model very well describes the lifetime statistics of long-lived resonances, provided that two effective parameters are appropriately renormalized. This renormalization is linked to the formation of short-lived resonances, a mechanism also known from the fractal Weyl law and the resonance-trapping phenomenon.

Variational calculations for anisotropic solitons in dipolar Bose-Einstein condensates

We investigate a multilayer stack of dipolar Bose-Einstein condensates in terms of a simple Gaussian variational ansatz and demonstrate that this arrangement is characterized by the existence of several stationary states. Using a Hamiltonian picture we show that in an excited stack there is a coupled motion of the individual condensates by which they exchange energy. We find that for high excitations the interaction between the single condensates can induce the collapse of one of them. We furthermore demonstrate that one collapse in the stack can force other collapses, too. We discuss the possibility of experimentally observing the coupled motion and the relevance of the variational results found to full numerical investigations.

Lifetime statistics in chaotic dielectric microresonators

A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits, which is analogous to the well-known bifurcation theory for periodic orbits and allows identifying the generic closed-orbit bifurcations of codimension 1. Several bifurcation scenarios are described in detail. They are shown to have as their constituents the generic codimension-1 bifurcations, which combine into a rich variety of complicated scenarios. We propose heuristic criteria for a classification of closed orbits that can serve to systematize the complex set of orbits.

Variational calculations on multilayer stacks of dipolar Bose-Einstein condensates

The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We present a semiclassical quantization of the hydrogen atom in crossed fields, which succeeds in resolving individual lines in the spectrum, but is restricted to the strongest lines of each n manifold. By means of a detailed semiclassical analysis of the quantum spectrum, we demonstrate that it is the abundance of bifurcations of closed orbits that precludes the resolution of finer details. They necessitate the inclusion of uniform semiclassical approximations into the quantization process. Uniform approximations for the generic types of closed-orbit bifurcations are derived, and a general method for including them in a high-resolution semiclassical quantization is devised.