# Project 4: Optimal preparation of many-body Rydberg states

## Summary

Faithful preparation of given many-body quantum states is an essential step towards realizing quantum technologies based on

the platform of Rydberg atoms. However, to accomplish such tasks is highly non-trivial given the limited coherence time of

Rydberg states.

The aim of this research project is to identify optimal control pulses for preparing several quantum many-body states in

Rydberg atoms fully taking into account relevant experimental considerations. The many-body quantum states to prepare include the

ground states of localized Rydberg atoms in a trap or an optical lattice, which will be used in the future for the experimental

investigation of quantum phenomena as well as of driven dynamics across the structural quantum phase transition (as predicted

by the Kibble-Zuerk mechanism), of crystalline states of Rydberg atomic gases and of various entangled states for quantum

information processing.

In all the above tasks, the pulse times should be shorter than the coherence times of the corresponding Rydberg states and

in the meanwhile, all the relevant experimental constraints, e.g. the laser energy, the bandwidth of control signal, and lattice

defects, among many others have to be fulfilled. To this end, we apply the dressed chopped random basis (dCRAB) optimal

control method, which iteratively improves the fidelity of the prepared state through updating the coefficients of the control

parameters expanded by some truncated randomized basis, to optimize the temporal shapes of the control pulses for our purpose.

Our research will provide an optimization toolbox to derive working control fields that steer the many-body Rydberg atomic

gases to target states, even approaching the quantum speed limit, which is defined as the minimum time scale for a given set

of external control fields to evolve the system in quantum states. On a more fundamental level, while efficiently preparing

interesting many-body states that cannot be obtained otherwise, our research will enable scientific explorations of many-body

physics on the Rydberg atomic gas platform.

## People

Prof. Dr. Tommaso Calarco, Institut für komplexe Quantensysteme, Universität Ulm