Interview with Cord Müller

Picture. Cord Müller, Dominique Delande and Martin Trappe

Who are you?

Cord Müller, Visiting Researcher (CNRS) at Institut Non Linèaire de Nice, France, and Visiting Professor at Universität Konstanz, Germany.

What prompted you to pursue this field of research?

While preparing a talk for the conference 'Disorder in condensed matter and ultra cold atoms' in Varenna, Italy, two years ago, I realised that a theoretical tool used by my collaborator Martin Trappe (CQT, Singapore, and CFT, Warsaw) in an entirely different project—on gradient corrections in density-functional theory—could be brought to work here as well. The task at hand is to compute the joint energy–momentum distribution of ultra cold matter waves in very strong random potentials. This distribution is required in order to link experimental data of cold-atom expansion experiments to the mobility edge, the critical energy that separates diffusive states from Anderson-localised states in strongly disordered potentials. And we are just beginning to exploit the fine capacities of cold atoms (and other experimental platforms, such as photonic systems) to gain a more detailed, dynamical understanding of Anderson's 'absence of diffusion' in random, possibly interacting systems.

What is this latest paper all about?

We have computed the Wigner–Weyl quantum corrections to the classical joint energy-momentum distribution, the so-called spectral function, of matter waves in spatially correlated random potentials. When Martin and I had completed the analytical estimates, we confronted them with high-quality numerical data by Dominique Delande (LKB, Paris). We found that, while the Wigner–Weyl corrections apply very accurately to standard Gaussian disorder, they are insufficient to describe the optical speckle potentials relevant for some cold-atom experiments.

What do you plan to do next?

In a direct follow-up to this project, we hope to get a better grip on the more singular semiclassical corrections for laser speckle potentials. More generally, Dominique and I are studying the diverse aspects of quantum dynamics around the Anderson-localisation mobility edge. With Martin and our colleagues from the Centre for Quantum Technologies (National University of Singapore), we still have to finish our above-mentioned project on the gradient corrections in density-functional theory!