Quantum chaos and disorder:
The majority of physical systems encountered in daily life are partially, sometimes even fully chaotic. The same principle applies in the quantum world where chaos may be induced by fabrication imperfections in quantum devices, impurities in condensed matter systems, or the chaotic dynamics of black holes. Quantum disorder and chaos 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. They are a source of fluctuations as much as of simplicity and universality. In chaotic dynamics microscopic details are ‘washed out’ which makes universal signatures such as dimensionality, symmetries, or topology stand out more clearly. This principle reflects in beautiful quantum field theories describing matter in the presence of chaos and disorder. Exploring chaos and disorder in condensed matter physics and more recently the physics of gravitational systems 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 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.