**Quantum technologies with Rydberg atoms**

Rydberg atoms are atoms in highly excited electronic states and exhibit extremely exaggerated properties compared to their ground state counterparts. For example, they exhibit a quasi-continuum of very strong dipole transitions in the terahertz and microwave range, and the lifetime of Rydberg states increases dramatically with their principal quantum number. This project explores how these properties can be harnessed for the efficient interconversion of millimeter-wave and optical fields [1,2], which has numerous applications in classical and quantum technologies. Furthermore, we explore how Rydberg ensembles can be used for the efficient generation and sensitive detection of millimeter waves.

[1] M. Kiffner, A. Feizpour, K. T. Kaczmarek, D. Jaksch and J. Nunn, *Two-way interconversion of millimeter-wave and optical fields in Rydberg gases*, New J. Phys. **18**, 093030 (2016).

[2] J. Han, T. Vogt, C. Gross, D. Jaksch, M. Kiffner, and W. Li, *Free-space microwave-to-optical conversion via six-wave mixing in Rydberg atoms*, Phys. Rev. Lett. **120**, 093201 (2018).

**Quantum materials in cavities for new quantum technologies **

This project considers quantum hybrid systems comprised of solid state materials that are strongly coupled to quantised modes of microwave (MW), terahertz (THz) or optical radiation. Quantum hybrid systems with a solid state component have the great advantage of being scalable since they inherit most of the production expertise developed for semiconductor devices. The overarching goal of this project is to advance the physics of solid state materials coupled to quantised radiation fields and to foster the development of novel quantum technologies emerging from these insights.

Of particular interest are quantum materials where small microscopic changes can result

in large macroscopic responses due to strong electron-electron interactions. Coupling these systems to cavities opens up the fascinating possibility of investigating the ultimate quantum limit where macroscopic properties of quantum materials are determined by quantum

light fields and vice versa.

As a paradigmatic example of these systems we consider the Fermi-Hubbard model and find that the electron-cavity coupling enhances the magnetic interaction between the electron spins in the ground-state manifold, introduces a next-nearest neighbour hopping and mediates a long-range electron-electron interaction between distant sites. In the manifold of states with one photon or one doublon excitation the cavity results in the formation of polariton branches. The vacuum Rabi splitting of the two outermost branches is collectively enhanced and can exceed the width of the first excited Hubbard band. The cavity-mediated modifications of the material properties in the ground and first excited manifolds can be experimentally observed via measurements of the magnetic susceptibility and the optical conductivity, respectively.

M. Kiffner, J. Coulthard, F. Schlawin, A. Ardavan, and D. Jaksch, *Manipulating Quantum Materials with Quantum Light*, arXiv:1806.06752.

**Solving real-world problems on a quantum computer**

This project is done in collaboration with IBM-Q. More details coming soon.