Quantum control of Rydberg ensembles

Ensembles of Rydberg atoms are an interesting system for quantum computation and metrology. In an ensemble of atoms all within Rydberg blockade distance, only one Rydberg excitation can exist at a time. This system is analogous to a Jaynes-Cummings model, with the collective qubit spin states corresponding to the cavity mode and the Rydberg excitation corresponding to the two-level system. This system is fully controllable by modulation of the qubit driving in the symmetric manifold. Starting from a spin coherent state, we can create any arbitrary Dicke state superposition using optimal control methods. We explore this system under various dressing regimes and look at the quantum speed limits. In the weak dressing limit, it is equivalent to a one-axis twisting model but in the strong dressing regime, higher order interactions dominate. They can be utilized for faster quantum control. Furthermore, this method can be used to encode qubits in the collective states of the atoms. We extend this to ensembles beyond the perfect Rydberg blockade regime.

[1] Keating, Tyler et al, Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles, Phys. Rev. Lett. 117, 213601 (2016)