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Annals of Physics

Entanglement in trapped Rydberg ions via engineered conical intersections and addressing of individual-ions

Abdessamad Belfakir, Yousra Bouasria, HERSCHEL A. RABITZ, Ahmed Ratnani

Published Jul 8, 2026• 0 citations
Publisher
DOI
10.1016/j.aop.2026.170617

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We demonstrate coherent control of motional dynamics in trapped Rydberg ions engineered to exhibit a conical intersection between adiabatic potential-energy surfaces. Using quantum optimal control, an optimally shaped electric field drives the motional wave packet between prescribed spatial configurations on microsecond timescales. Localized nonadiabatic coupling breaks the symmetry of the dynamics and produces a directed trajectory: after only a few early passages through the conical intersection region, the packet proceeds toward the target with high fidelity. In contrast, in the Born-Oppenheimer limit, where such coupling is absent, the optimized control yields symmetric, multicycle oscillations rather than a comparably directed displacement. While both approaches reach the target at the chosen final time, the underlying trajectories are qualitatively different. This work demonstrates that engineered conical intersections can serve as a potential control resource for directional motional dynamics, complementing pulse-shaping methods in trapped-ion systems. This directional motion of the ions, enabled by the conical intersection, may provide a route toward improved control of motional states in trapped-ion quantum information processing.
We study spin-phonon coupled dynamics in the vicinity of a sloped conical intersection created by laser coupling the electronic (spin) and vibrational degrees of freedom of a pair of trapped Rydberg ions. We show that the shape of the potential energy surfaces can be engineered and controlled by exploiting the sideband transitions of the crystal vibration and dipole-dipole interactions between Rydberg ions in the Lamb-Dicke regime. Using the sideband transition, we realize a sloped conical intersection whose cone axis is only tilted along one spatial axis. When the phonon wavepacket is located in the potential minimum of the lower potential surface, the spin and phonon dynamics are largely frozen owing to the geometric phase effect. When starting from the upper potential surface, the electronic and phonon states tunnel to the lower potential surface, leading to a partial revival of the initial state. In contrast, the dynamics drastically change when the initial wavepackets are away from the conical intersection. The initial state is revived, and is almost entirely irrelevant to whether it is from the lower or upper potential surface. Complete Rabi oscillations of the adiabatic states are found when the wavepacket is initialized on the upper potential surface. The dynamics occur on the microsecond and nanometer scales, implying that Rydberg ions provide a platform for simulating nonadiabatic processes in the vicinity of a sloped conical intersection.
Conical intersections between electronic potential energy surfaces are paradigmatic for the study of nonadiabatic processes in the excited states of large molecules. However, since the corresponding dynamics occurs on a femtosecond timescale, their investigation remains challenging and requires ultrafast spectroscopy techniques. We demonstrate that trapped Rydberg ions are a platform to engineer conical intersections and to simulate their ensuing dynamics on larger length scales and timescales of the order of nanometers and microseconds, respectively; all this in a highly controllable system. Here, the shape of the potential energy surfaces and the position of the conical intersection can be tuned thanks to the interplay between the high polarizability and the strong dipolar exchange interactions of Rydberg ions. We study how the presence of a conical intersection affects both the nuclear and electronic dynamics demonstrating, in particular, how it results in the inhibition of the nuclear motion. These effects can be monitored in real time via a direct spectroscopic measurement of the electronic populations in a state-of-the-art experimental setup.