Quantum chaos and disorder:

Apart from few simple exceptions, the majority of physical systems encountered in daily life are ‘non-integrable’ and are partially, sometimes even fully chaotic. The same principle holds true in the quantum world where chaos may be induced by fabrication imperfections in quantum devices, impurities in condensed matter systems, or complex interactions in molecules. Disorder and chaos in quantum systems generate a multitude of phenomena including strong quantum fluctuations in observables, single and many particle quantum localization, and various types of unique quantum phase transitions. In particular, they are a source of simplicity and universality. For example, in a disordered metal, microscopic details of the underlying lattice structure are ‘washed out’ which makes universal structures depending only on dimensionality, symmetries, or topology stand out more clearly. This principle reflects in the structure of various beautiful quantum field theories describing matter in the presence of chaos and disorder. Exploring the physics of chaos and disorder in condensed matter and cold atomic systems within such theoretical frameworks is one of our main research activities.

(Disordered) topological quantum matter:

The physics of topological phases of matter has become one of the most exciting fields of modern physics. Our group explores the properties of topological quantum matter under the real life condition that translational invariance is broken by material imperfections and disorder. How can we understand the robustness of topology in disordered systems? Topological invariants are routinely computed with reference to crystal momenta — how do we describe them if translational invariance is absent and crystal momenta are no longer defined? And how do we understand the physics of topological phase transitions driven by disorder? These are examples of questions are central to our recent work in the field.

Blueprints for topological quantum information
devices:

We will soon see the realization of novel quantum bits based on the Majorana fermion state. This opens exciting perspectives for the design of powerful architectures for quantum information processing. Our group is working along various directions towards this long term goal. This includes the proposal of efficient diagnostics probing the basic functionality of Majorana qubits. And the design of advanced architectures linking multiple qubits into stabilizer codes or quantum simulators.