Julian Böhm

Dynamically encircling an exceptional point for asymmetric mode switching.

Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an ‘exceptional point’ occurs, giving rise to fascinating phenomena that defy our physical intuition. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly, such as a state-flip or the accumulation of a geometric phase. The topological structure of exceptional points has been experimentally explored, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.

Microwave Experiments Simulating Quantum Search and Directed Transport in Artificial Graphene

A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to √N, where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grovers original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density-namely, at or near the Dirac point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains.

Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity

Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an ‘exceptional point’ occurs, giving rise to fascinating phenomena that defy our physical intuition. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly, such as a state-flip or the accumulation of a geometric phase. The topological structure of exceptional points has been experimentally explored, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.

Focusing inside Disordered Media with the Generalized Wigner-Smith Operator

We introduce a wave front shaping protocol for focusing inside disordered media based on a generalization of the established Wigner-Smith time-delay operator. The key ingredient for our approach is the scattering (or transmission) matrix of the medium and its derivative with respect to the position of the target one aims to focus on. A specific experimental realization in the microwave regime is presented showing that the eigenstates of a corresponding operator are sorted by their focusing strength-ranging from strongly focusing on the designated target to completely bypassing it. Our protocol works without optimization or phase conjugation and we expect it to be particularly attractive for optical imaging in disordered media.

Wave front shaping in quasi-one-dimensional waveguides

Using 10 monopole antennas reaching into a rectangular multi mode waveguide we shape the incident wave to create specific transport even after scattering events. Each antenna is attached to an IQ-Modulator, which allows the adjustment of the amplitude and phase in a broad band range of 6-18 GHz. All of them are placed in the near field of the other, thus the excitation of an individual antenna is influenced by the presence of the other antennas. Still these 10 antennas are sufficient to generate any combination of the 10 propagating modes in the far field. At the output the propagating modes are extracted using a movable monopole antenna that is scanning the field. If the modes are scattered in a scattering region, the incident wave can be adjusted in such a way, that the outgoing wave can still be adjusted as long as localization is not present.