Calculation of Rydberg interaction potentials
The strong interaction between individual Rydberg atoms provides a powerful tool exploited in an ever-growing range of applications in quantum information science, quantum simulation and ultracold chemistry. The starting point of this project was that more and more experiments are probing this interaction at short atomic distances or with such high precision that perturbative calculations as well as restrictions to the leading dipole–dipole interaction term are no longer sufficient. We wrote a tutorial, reviewing all relevant aspects of the full calculation of Rydberg interaction potentials such as the derivation of the interaction Hamiltonian from the electrostatic multipole expansion, numerical and analytical methods for calculating the required electric multipole moments, and the inclusion of electromagnetic fields with arbitrary direction. Our software for calculating Rydberg potentials including all features discussed in this tutorial is available as open source.
Accurate mapping of Rydberg atoms on interacting spin-1/2 particles
The goal of this project was to study a system of atoms that are laser-driven to nD3/2 Rydberg states and assess how accurately they can be mapped onto spin-1/2 particles for the quantum simulation of anisotropic Ising magnets. Using non-perturbative calculations of the pair interaction potentials between two atoms in the presence of both electric and magnetic fields, we emphasized the importance of a careful selection of the experimental parameters in order to maintain the Rydberg blockade and avoid excitation of unwanted Rydberg states. We then benchmarked these theoretical observations against experiments using two atoms. Finally, we showed that in these conditions, the experimental dynamics observed after a quench is in good agreement with numerical simulations of spin-1/2 Ising models in systems with up to 49 spins, for which direct numerical simulations become intractable.