# Theory Research

# PROJECTS

# Magnetic trapping of highly excited (Rydberg) atoms

Rydberg atoms are highly excited atoms whose size can be of the order of several 100 nanometres. This is comparable with the typical length scale of magnetic traps that are used in ultra cold atoms experiments. Therefore Rydberg atoms cannot be treated as point-like particles. This has non-trivial consequences for their trapping properties which is of importance for current experiments that employ Rydberg atoms for implementing quantum information protocols.

# Quantum gates with highly excited (Rydberg) atoms

Rydberg atoms interact strongly even over distances of several micrometres. 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 a digital quantum simulator for complex spin models.

# Dynamics of strongly interacting Rydberg gases

When atoms in a dense gas are irradiated by a laser, which is resonant to a transition to a Rydberg state, only a small fraction of atoms is actually excited. This phenomenon is known as the dipole- or Rydberg-blockade. It arises from the strong interaction between two Rydberg atoms which effectively shifts the state in which both atoms are excited out of resonance. Thus this state cannot be accessed by the laser and only one atom can be excited at a time. This mechanism leads to a strongly correlated excitation dynamics in a dense atomic gas. Such system allows to study thermalisation of a closed quantum system and the creation of correlated and entangled atomic states. The latter are potentially useful for quantum information processing, single photon generation and precision measurements.

# Dynamical phase transitions in open quantum systems

Equilibrium statistical mechanics provides the tools to study equilibrium phases and phase changes in many body systems. Thermodynamic phases are characterised by average values of thermodynamic observable, such as volume in a liquid or magnetisation 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.

# Electronic dynamics of highly excited ion crystals

In certain ion traps electronically highly excited states exist in which an electron is delocalised among two ions thereby forming a giant molecule of several micrometre size. In a certain energy window these molecular states can be regarded as superpositions of Rydberg states of individual ions. In this 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 tunnelling 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 micrometres.