# Research

Ultracold quantum gases and in particular Bose-Einstein condensates opened up the exploration of quantum phenomena in the regime between the micro- and macrocosmos. The past five to ten years have seen enormous progress with respect to our knowledge on the properties and phenomena in condensed atomic clouds. The existing technologies and perspectives to coherently control and process ultracold matter waves manifest themselves in a diversity of areas such as atom optics, quantum information processing, ultracold Rydberg gases and many more.

Our theory group focuses on several aspects of ultracold atomic and molecular systems which have received major attention during the past years and introduce additional flexibility and diversity to the area of ultracold physics in general. Specifically this covers the investigation of:

Photo: AG Schmelcher

## Ultracold Rydberg Atoms

Among the many fascinating systems encountered in modern ultracold atomic and molecular physics are Rydberg atoms. Rydberg atoms are (in the framework of ultracold physics almost exclusively alkali-)atoms in states of high principal quantum number (more)

Photo: AG Schmelcher

## Nonequilibrium Quantum Dynamics of Correlated Ultracold Bosonic and Fermionic Ensembles

Ultracold atoms represent an ultimate toolbox to study fundamental quantum processes in physics with potential applications to technology (e.g. sensoring, quantum information processing). Design of the external trapping geometries and control of the interparticle interactions are possible with high precision using appropriately designed electric (laser) and magnetic fields (more)

Photo: AG Schmelcher

## Nonlinear Excitations in Bose-Einstein Condensates

Ultracold atomic gases in the condensed phase represent macrosopic quantum states of many-body systems that can be described theoretically on a mean-field level by the so-called Gross-Pitaevskii equation. The latter extends the nonlinear Schroedinger equation thereby including mesoscopic environments such as traps. Our focus in these systems are nonlinear excitations. For quasi one dimensional systems the lowest excited states are solitonic states (more)

Photo: AG Schmelcher

## Quantum Scattering in Confined Geometries

Dimensionality represents a key issue for few- and many-body systems. Depending on whether one, two or all three dimensions are strongly confined the properties and dynamics of interacting bosons show very different features. Modern experiments on ultracold bosonic systems (more)

Photo: AG Schmelcher

## Ultracold Polar Molecules in External Fields

Over the past decade investigations of ultracold quantum gases have been revealing a wealth of intriguing phenomena. In particular, ultracold molecular systems represent a paradigm including molecular Bose-Einstein condensates. External fields on the other hand are equally important for the preparation and control of ultracold systems. They are used for cooling and trapping as well as for quantum state preparation or the tuning of (more)

Photo: AG Schmelcher

## Quantum and Classical Dynamics of Driven Billiards and Lattices

We study the classical and quantum dynamics of (periodically) driven systems. Typical model systems are one-dimensional extended lattices of individually driven barriers or two-dimensional billiards with time-dependent boundaries. Due to the driving, these systems are pushed out of equilibrium. This allows the study of non-equilibrium dynamics such as diffusion in momentum space e.g. Fermi acceleration, or - in the case of spatially extended systems (more)

Photo: AG Schmelcher

## Computational Quantum Transport in Mesoscopic Systems

The ability to reduce the size of electronic circuits to the nanometric scale has lead to increasing interest in the properties of electron transport in the mesoscopic regime, and its dependence on externally tuned ... (more)

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## Atoms and Molecules in External Fields

The group has a traditional focus on atomic and molecular sytems exposed to magnetic, electric and electromagnetic fields. Effects due to the coupling of the center of mass and internal motion of atoms and molecules, such as giant dipole states in crossed fields or self-ionization of moving ions, are examples for the intriguing processes occuring in combined fields. Strong field effects in atomic and molecular system, particularly their impact on the electronic structure, belong to the traditional areas of the group.

Photo: AG Schmelcher

## Symmetry breaking and local symmetries

We have recently developed a theory of local symmetries that is capable of describing wave mechanical systems (photonics, acoustic and quantum mechanics) in an environment of spatially varying symmetries. Focusing on the case of translations and parity we have found a systematic pathway for the breaking of discrete symmetries via non-local invariant currents and discovered a generalization of the well-known Bloch and parity theorems. This is the beginning of a new research direction that aims at describing complexity via composite symmetric systems with novel rules for the creation of wave mechanical structures. One example is the recently suggested completely locally symmetric materials that allow for a classification of their perfectly transmitting resonances in the framework of the above-mentioned invariant currents.

Photo: AG Schmelcher

## Curved helical structures

Low dimensional structures are of fundamental physical importance, since they often exhibit a highly unconventional behaviour, giving rise to novel effects, such as the quantum Hall effect or the high temperature superconductivity. Geometry adds to the complexity of such structures, while offering, at the same time, means of tunability and control. We study properties of low dimensional systems, possessing a non-trivial geometry, both at a classical and a quantum level... (more)

Photo: AG Schmelcher

## Hybrid atom-ion quantum systems

Hybrid atom-ion systems represent a new and excellent platform to explore new physics that the two systems separately would not permit. For instance, the investigation of ultracold elastic and inelastic atom-ion collisions and controlled chemical reactions, but also the realisation of quantum information processing, where the advantages of charged and neutral particles are combined. In addition to this, atom-ion systems are very suited to simulate condensed-matter systems and Fröhlich polaron Hamiltonians more closely, where, for example, the charge-phonon, an important ingredient of solid-state systems, is naturally mimicked in such hybrid atomic system... (more)