Generating particle-like scattering states in absorptive wave transport

In a very recent work by one of the applicants it was shown how to systematically generate particle-like scattering states in wave transport through complex scattering systems [PRL 106, 120602 (2011)]. These beam-like states have a number of interesting properties like a highly collimated wave function and deterministic values of transmission through a system. In particular, as the construction of such states requires only the knowledge of a system`s scattering matrix (rather than of its geometric details) this new theoretical concept promises to be a very useful tool for the experiment (see, e.g., the discussion of the above theory paper at http://focus.aps.org/story/v27/st13 and in the June 2011 issue of "La recherche"). These special wave states can be useful in any situation in which a wave signal needs to be transmitted from one point to another without losing part of the signal to the environment. Such properties are of importance for saving power in the signal transmission, for security issues (to avoid eavesdropping), for improving the signal quality as well as for the focusing of waves on a small spot. In view of such a broad range of possible applications we propose in this project to realize such particle-like wave states experimentally. Ideal setups for this purpose are microwave experiments for which the French project partner (Ulrich KUHL) has acquired extensive expertise. Microwave measurements have been widely used to investigate complex open systems, as the components of the scattering matrix can here be measured including phases. Especially in quasi-two-dimensional cavities the complex scattering state and the energy flow inside is accessible by scanning the system with an antenna. To generate the injected particle-like scattering states the high dimensional scattering matrix in mode representation will be determined. For this purpose the transport through the system for different antenna positions in the leads is measured and the scattering matrix is obtained by Fourier transform [PRB 83, 134203 (2011)]. Following the theoretical calculations based on the measured scattering matrix the state in the incoming lead will be shaped by a tunable antenna array. A probe antenna will be used to verify if the resulting scattering state is, indeed, concentrated on the trajectory of a classical particle. For its realization, the above goal will require strong theoretical support which will be the responsibility of the Austrian project partner (Stefan ROTTER). In particular, first questions to be addressed from the theoretical side will be focused on all the imperfections that an experiment typically comes along with. For this purpose the theoretical concepts devised for a perfectly unitary scattering system will have to be extended to include effects like noise, dissipation and the situation that only a sub-part of the system`s scattering matrix is known. This extension is crucial to create these states experimentally. In the second part of the project, we will study the stability of the created states with respect to external perturbations. Explicit time-dependent wave packets as well as multi-lead cavities will be studied in close collaboration with the experiment and ways will be explored to create scattering states with a maximal time-delay such that these waves will be almost perfectly absorbed [PRL 107, 163901 (2011)]. Finally the relation of the particle-like scattering states with Gaussian as well as diffraction-free Bessel beams will be investigated.

No matter whether it is acoustic waves, quantum matter waves or optical waves of a laser all kinds of waves can be in different states of oscillation, corresponding to different frequencies. Calculating these frequencies is part of the tools of the trade in theoretical physics. Recently, however, a special class of systems has caught the attention of the scientific community, forcing physicists to abandon well-established rules. When waves are able to absorb or release energy, so-called "exceptional points" occur, around which the waves show quite peculiar behaviour: lasers switch on, even though energy is taken away from them, light is being emitted only in one particular direction, and waves which are strongly jumbled emerge from the muddle in an orderly, well-defined state. Rather than just approaching such an exceptional point, the theory group of Stefan Rotter (TU Wien, Austria) together with the experimental team around Ulrich Kuhl (Nice University, France) have now managed for the first time to steer a system around this point, with remarkable results that have been published in the journal "Nature [1]. Exceptional points occur, when the shape and the absorption of a system can be tuned in such a way that two different waves can meet at one specific complex frequency. At this exceptional point the waves not only share the same frequency and absorption rate, but also their spatial structure is the same. One may thus really interpret this as two wave states merging into a single one at the exceptional point. In the specific project carried out with funding from the FWF two different wave modes were sent through a wave guide that is tailored not only to approach the exceptional point, but actually to steer the waves around it. No matter which one of the two possible modes is coupled into the system at the output, always the same mode emerges. When waves are coupled into the waveguide from the opposite direction, the other mode is favoured. Due to the collaboration with the experimental team in Nice, these exciting results could immediately be implemented in a laboratory experiment involving suitably designed waveguides for microwaves, where the predicted behavior was now indeed observed. Systems with exceptional points open up an entirely new class of possibilities for controlling waves. Indeed, several research groups all over the world are currently working on exceptional points and one can expect to hear soon much more about them in many different areas of physics. [1] Jörg Doppler, Alexei A. Mailybaev, Julian Böhm, Ulrich Kuhl, Adrian Girschik, Florian Libisch, Thomas J. Milburn, Peter Rabl, Nimrod Moiseyev, Stefan Rotter (2016). "Dynamically encircling an exceptional point for asymmetric mode switching". Nature 537, 76 (2016).