Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles

TL;DR

This paper demonstrates that symmetric Rydberg ensembles can be fully controlled to generate arbitrary superpositions of Dicke states using microwave-driven phase control, enabling high-fidelity state preparation within microseconds.

Contribution

It introduces a method for complete controllability of symmetric Rydberg ensembles to produce arbitrary Dicke states, including a dressed ground control scheme to simplify implementation.

Findings

Arbitrary symmetric states of ~10 hyperfine qubits can be generated with high fidelity.

Control can be achieved within approximately 1 microsecond with current technology.

The dressed ground control scheme reduces phase switching requirements.

Abstract

Symmetric ensembles of neutral atoms interacting via the Rydberg blockade are well-described by the Jaynes-Cummings Hamiltonian. We use this framework to study the problem of generating arbitrary superpositions of Dicke states of hyperfine qubits in such ensembles. The combination of the symmetric Rydberg blockade and microwaves that drive the qubits with a time-dependent phase is sufficient to make these ensembles completely controllable, in the sense that one can generate an arbitrary unitary transformation on the system. We apply this to the problem of state mapping. With currently feasible parameters, it is possible to generate arbitrary symmetric states of ~ 10 hypefine qubits with high fidelity in ~ 1 microsecond, assuming fast microwave phase switching times. To reduce the requirements on phase switching, we propose a "dressed ground control" scheme, in which the control task is simplified by restricting the system's dynamics to the dressed ground subspace.