Generating particle-like scattering states in absorptive wave transport

In a very recent work by the project coordinator 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 will address in this project a concrete realization of such particle-like wave states. Ideal setups for this purpose are microwave experiments for which the French project partner (Ulrich KUHL, Nice) 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 coordinator (Stefan ROTTER, Vienna). 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.