The strong dipole transition between high-lying Rydberg states of hydrogen-like atoms and bound excitons is the source of long-range interaction between them. The most notable manifestation of Rydberg-Rydberg interaction is the Rydberg blockade effect where exciting one atom (exciton) can prevent any other excitation in a certain vicinity. Here, we share our results on simulation of Rydberg exciton dynamics and its application in simulation of quantum many-body dynamics where we show a $Z_{2}$-ordered phase can be reached by addressing Rydberg states of excitons in cuprous oxide (arxiv:2107.02273). In the second part, look into application of quantum control in a Rydberg system of few atoms to reach desired (non-trivial) quantum states such as cluster states. We then apply this approach to simulate a particular small-scale circuit that enables encoding a single qubit into error-correcting states.

This is joint work with Jacob Taylor, Sumit Goswami, Valentin Walther, Michael Spanner, Christoph Simon, Valerio Crescimanna, and Aaron Goldberg. This work was supported by NSERC Discovery Grant.