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arXiv:2607.26978

Mean-field Pulse Adaptation for the Circularization of Interacting Rydberg Atoms

Matthias Hüls, Felix Motzoi, Tommaso Calarco, Eloisa Cuestas

quant-phphysics.atom-phSubmitted Jul 29, 2026• Announced Jul 30, 2026• 0 citations• Revised Jul 30, 2026 (v2)
v1 · Jul 29, 2026v2 · Jul 30, 2026
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Abstract

Arrays of circular Rydberg atoms provide a promising platform for quantum simulation and computation; however, their preparation in the presence of interatomic interactions remains a major challenge. While optimal control methods have enabled the design of fast and accurate radio-frequency pulses for the circularization of a single atom and of an atom pair, the extension to more atoms is fundamentally limited by the exponential growth of the Hilbert space, which renders numerical simulations computationally infeasible. Here, we introduce an effective model that treats interactions within a mean-field approximation, thereby enabling the simulation of large atomic systems. Our model further enables the adaptation of pulses optimized for non-interacting atoms to interacting systems, based on the computation of a single time evolution. For two interacting $^{87}\mathrm{Rb}$ atoms, we demonstrate that the error of our method remains below $1 \, \%$ and that our adapted pulses recover the initial performance of optimal pulses in the regime of weak to moderate interaction strengths.

Comments
5 pages, 2 figures

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Preparation of a so-called circular state in a Rydberg atom where the projection of the electron angular momentum takes its maximum value is challenging due to the required amount of angular momentum transfer. Currently available protocols for circular state preparation are either accurate but slow or fast but error prone. Here we show how to use quantum optimal control theory to derive pulse shapes that realize fast and accurate circularization of a Rydberg atom. In particular, we present a theoretical proposal for optimized radio-frequency pulses that achieve high fidelity in the shortest possible time, given current experimental limitations on peak amplitudes and spectral bandwidth. We also discuss the fundamental quantum speed limit for circularization of a Rydberg atom when lifting these constraints.
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Summary form only given. Quantum simulation offers a highly promising way to understand large correlated quantum systems, and many experimental platforms are now being developed. Rydberg atoms are specially appealing thanks to their strong and short-range dipole-dipole interaction and to their long lifetime. Low-angular momentum Rydberg atoms have been successfully used recently to realize early quantum simulators. These experiments suffer, however, from the limited (despite long) lifetime of these levels and the fact that they cannot be efficiently trapped [1, 2].Here, we propose to use circular Rydberg atoms, i.e., Rydberg atoms with maximum angular momentum, to realize a quantum simulator: A chain of circular atoms is laser trapped inside a spontaneous emission inhibiting structure. A defect-free chain of 40 atoms could be prepared. It is expected to live several seconds inside the inhibition structure. Given the strong interaction frequencies between nearby Rydberg atoms, such a system would, thus, allow us to observe the dynamics of the spin chain over several 10 4 interaction cycles. In addition, the solid state Hamiltonian that would be simulated is fully tuneable experimentally. The proposed circular atoms quantum simulator should therefore open the way towards the simulations of systems and of their dynamics beyond the grasp of classical computation.
Circular Rydberg atoms, with their long lifetimes and adjustable strong dipolar interactions, are promising candidates for the implementation of quantum simulations in regimes that were previously out of reach. A new quantum simulator paradigm, based on qubits encoded in circular states, would implement an XXZ spin-1/2 Hamiltonian with dynamically adjustable parameters over a wide range of values. This thesis addresses the preliminary steps in constructing such a quantum simulator. First, we present the realization of two-dimensional arrays of optically-trapped circular Rydberg atoms with arbitrary geometries. For this purpose, we prepare arrays of ultra-cold rubidium atoms, individually trapped in optical tweezers. An additional beam with adjustable position allows us to rearrange the atoms within the array to implement the desired geometry in a deterministic manner. We then excite the atoms to the circular state with principal quantum number n=52, while trapping them in hollow beams using the ponderomotive force. These experimental capabilities allowed us to control and characterize, for the first time, the dipolar interactions between circular states, within pairs of individually trapped atoms. We showed the good agreement of these measurements with theoretical expectations and highlighted their dependence on the system's geometry. This experimental study is coupled to an investigation of the motion of the circular atoms within their traps.
Neutral-atom systems are promising platforms for quantum simulation and computation, owing to their long coherence times. However, their intrinsically weak ground-state interactions pose a major limitation to the advancement of scalable quantum simulation and computation. To address this challenge, we propose an approach to enhancing the ground-state interaction strength of neutral atoms via Floquet modulation of a Rydberg atomic ensemble. Each Floquet period consists of ground-state coupling followed by a pulse driving the transition from the ground state to the Rydberg state. Theoretical analysis and numerical simulations demonstrate that after a defined evolution time, neutral atoms within Rydberg ensembles can collectively form a W state in the ground-state manifold. Even when the Rydberg interaction strength is far below the blockade regime, the fidelity remains remarkably high. Finally, we analyze the application of this scheme in the preparation of single-photon sources. In general, our proposed mechanism offers an efficient and highly controllable method for quantum state preparation within the Rydberg atomic ensembles, significantly enhancing the accuracy and stability of quantum state engineering while providing a well-controlled quantum environment for single-photon generation.