## Research topics

**Cold atoms for quantum simulation of complex dynamical processes**

Highly excited atoms, so-called Rydberg atoms, are one of the most modern manifestations of cold atomic quantum systems. They form a physical basis for the implementation of quantum information processing protocols, the creation of synthetic forms of matter as well as the simulation of complex quantum processes. We are interested in developing the theoretical foundations of interacting ensembles of Rydberg atoms to advance the theoretical understanding of collective phenomena in interacting many-body quantum systems. These include the study of phase transitions, the dynamics of localisation phenomena, time-crystals, thermalisation, the emergence of long timescales, non-ergodicity and glassiness as well as applications for enhanced sensing and quantum information applications.

**Quantum soft-matter physics**

Cold gases of Rydberg atoms feature so-called kinetic constraints which in soft-matter physics are used to model glassy substances. Kinetic constraints are often thought of as being merely an effective construct, forming the basis of highly idealised glass models. Their natural occurrence in Rydberg gases paves the way towards realising and studying quantum versions of classical non-equilibrium processes, such as epidemic spreading of diseases or predator-prey population dynamics. Introducing quantum effects in these settings has been shown to give rise to the emergence of new forms of collective behaviour, e.g. manifesting in new universal behaviour near phase transitions.

**Open many-body quantum systems and thermodynamics of quantum jump trajectories**

Equilibrium statistical mechanics provides the tools to study equilibrium phases and phase changes in many body systems. Thermodynamic phases are characterized by average values of thermodynamic observables, such as volume in a liquid or magnetization in a magnet, which are controlled by conjugate fields, such as pressure or magnetic field. Non-analyticities in free-energies correspond to phase transition points, and the proximity to a phase transition manifests in large and rare fluctuations of observables around their thermodynamic values. An analogous perspective can be adopted for the study of dynamical phases in non-equilibrium systems by applying the large-deviation method. The large-deviation formalism allows to treat ensembles of trajectories, classified by dynamical order parameters or their conjugate fields, in the same way that equilibrium statistical mechanics treats ensembles of configurations. Important properties of classical non-equilibrium systems can be uncovered by exploiting this analogy, such as the existence of "space-time" phase transitions in glassy systems. This approach can also be applied to quantum non-equilibrium systems. It reveals important properties of ensembles of trajectories of quantum systems that undergo quantum jumps in some form, such as driven quantum systems weakly coupled to a thermal bath. Surprisingly, one can observe features of dynamical crossovers and dynamical phase transitions even in quantum systems with only a few degrees of freedom.

**Quantum information processing with highly excited (Rydberg) atoms**

Rydberg atoms interact strongly even over distances of several micrometers. This allows the implementation of multi-particle quantum gates which enable a single atom to control the quantum state of a whole ensemble of atoms located it its vicinity. Such gate is not only useful in the quantum information context but also constitutes an essential ingredient of digital quantum simulators for complex spin models.

**Electronic dynamics of highly excited ion crystals**

In certain ion traps electronically highly excited states exist in which an electron is delocalized among two ions thereby forming a giant molecule of several micrometer size. In a certain energy window these molecular states can be regarded as superpositions of Rydberg states of individual ions. Inthis system it is possible to observe coherent charge transfer, i.e. beyond a critical principal quantum number the electron can coherently tunnel through the Coulomb barrier to an adjacent doubly charged ion. The tunneling occurs on timescales on which the dynamics of the nuclei can be considered frozen and radiative decay can be neglected. Such system is interesting since it represents a step towards the implementation of electronic Hubbard models in an ion trap setup. Moreover, it allows to perform "chemistry" and "molecular physics" at macroscopic length scales since trapped ions have a typical interparticle spacing of a few micrometers.

**Enhanced nuclear magnetic resonance far from equilibrium**

A current theme in nuclear magnetic resonance (NMR) is the exploitation of non-equilibrium approaches – so-called hyperpolarisation methods – for enhancing the sensitivity of magnetic resonance imaging. One such method is dynamic nuclear polarisation which promises a million-fold enhancement over standard approaches. The underlying mechanism makes use of microwave-driven paramagnetic centres (electrons) that transfer their polarisation (magnetisation) to adjacent nuclei via dipole-dipole interaction. Polarisation is then built up in the bulk of nuclei via diffusion. We developed an approach for modelling the underlying dynamics which allows us to simulate the polarisation build-up in large nuclear ensembles (thousands of spins) and moreover shows that so-called kinetic constraints are at the heart of this non-equilibrium evolution. This establishes on a theoretical level that polarisation within the bulk of nuclei is built up diffusively. Moreover, these findings make a direct connection between NMR and the physics of glasses. This opens a new perspective on the microscopic dynamics of hyperpolarisation but also puts in reach it's systematic optimisation, e.g. by providing guidance for the design of employed agents.