Abstract: A review on the most recent activities in Rydberg physics at the
center for optical quantum technologies will be provided. I start
out with addressing the exotic properties of ultralong-range Rydberg
molecules (ULRM). ULRM possess extreme bond lengths of the order
of several micron and huge dipole moments. Their potential energy
curves mimic the highly oscillatory structure of the Rydberg wave
function thereby offering new possibilities for engineering molecular
properties on vastly different time and length scales. Trilobite and
butterfly states can easily be controlled by weak external electric
or magnetic fields. I demonstrate that synthetic dimensions based
on quantum numbers can be used to design conical intersections and
consequently non-adiabatic interaction effects in the spectra of
ULRMs. Ultrafast decay processes are a consequence of these intersections.
Quenches of external fields then lead to a rich rovibrational
quantum dynamics of ULRM.
The second part of this talk focuses on quantum simulation and
quantum optimization. I provide evidence for novel quantum phases
of strongly interacting many-body Rydberg setups, specifically the
so-called bond order density wave is unraveled and the extended
control of Luttinger liquid phases is presented. On the quantum
optimization side I describe how a local detuning approach can
enhance the tweezer array-based control of the famous graph
theoretical MIS and Max-Cut problems. The traditional order $\propto N^2$
approach is here replaced by a linear system size scaling approach.
Finally, I will make a short excursion into our recent work on
single atom implementation of integer linear programming. Here,
a single Rydberg atom will be used to encode linear and even
nonlinear integer problems which are known to be difficult
to solve in a classical manner.