The non-linear dynamics and complex system research group of Joachim Burgdörfer (JB) is concerned with theoretical investigations of complex quantum and classical dynamics with applications in the field of photonics, atomic, surface and condensed-matter physics. Complexity is the ubiquitous hallmark of systems in which strong interactions prevent the reduction and separability in terms of independent-particle models or reduced degree of freedom models. Prototypical examples include the chaotic dynamics of classical non-linear systems and entangled correlated dynamics in quantum systems. Underlying concepts and methods developed lend themselves to application in a wide range of fields such as surface and condensed matter physics and photonics represented in Solids4Fun.
Specific focus is on the theoretical investigation of ultrafast light-matter interaction and its implementation for probing, controlling and manipulation of electronic and molecular dynamics. The ultimate goal is to understand electronic dynamics on the atto- and femtosecond scale in atoms and at surfaces. Key to control and functionalization are the non-linearity of the response to intense ultrashort pulse which poses challenge to current theory. Exchange between theory and experience is of central importance as an enabling feature both on the research and on the doctoral training level.
The group of Joachim Burgdörfer has developed a variety of methods and simulation codes. They include an embedded cluster approximation (ECA) based on advanced wave function quantum-chemistry methodology implemented in collaboration within H. Lischka (partner within SFB-VICOM). It allows the descriptions of scenarios where correlation effects are crucial and where the Born-Oppenheimer approximation, the foundation of most quantum mechanical simulations, breaks down. Current applications address wide-band gap insulators, structural defects, and adsorbates investigated in the surface group of Ulrike Diebold.
Time-dependent density functional theory (TDDFT) as well as classical trajectory Monte Carlo (CTMC) methods have been implemented with applications to time-resolved photoemission from surfaces by few-cycle infrared and sub-fs XUV pulses. A current PhD project explores the interconnection between ultrashort time scale and nanometer length scale which promises novel avenues of light-matter interaction with potential applications to both optical systems and functionalization of matter. The emerging field of nanoplasmonics is a prime example. The group of Joachim Burgdörfer simulates the interaction of few-cycle infrared pulses with metallic nanotips. The field enhancement by the dielectric response within the nano-scaled confined geometry enhances the sub-cycle tunnel ionization. This effect can be used to determine the carrier-envelope phase of the light as well as the size and local properties of the nanotip but also to modify the light field on the nanoscale.
A full ab-initio treatment of dynamical correlation effects is possible for excitation of few-electron atoms (prominent example helium) by ultrashort XUV and IR pulses giving access to ground-state and excited final-state correlations including entangled two-electron wavepackets in the continuum. The FEDVR solver based on the short interactive Lanczos-Arnoldi algorithm implemented in the group allows for the accurate simulation of multi-electron excitations. This research is closely connected to the photonics group of Andrius Baltuska.
Quantum dynamics embedded in an open environment is subject to ubiquitous decoherence eventually destroying entanglement and rendering the system classical. Understanding and, eventually, controlling decoherence is crucial for functionalized quantum matter ranging from coherent control to quantum information proceeding. The group has developed the quantum trajectory Monte Carlo (QTMC) method and echo-like protocols for pulse sequences to revert dephasing and enhancing revivals in Rydberg ensembles. Dephasing of ensembles of optically excited NV in diamonds due to inhomogeneous line broadening of the ensemble is investigated by the group of Johannes Majer which whom collaborations are under way.