Filtering Rydberg Interactions in Space - Programmable Peaks at Target Separations

Long-range Rydberg interactions are widely used in QTechnology [1-19] but create cross-talk: atoms that are not meant to interact still shift one another, limiting parallel gate execution and constraining many-body design. We propose a resonantly driven “interaction filter” that converts the usual long-range coupling into a sharply localized interaction that turns on only near a programmable interatomic separation [20]. The mechanism is an interaction-induced resonance: at one selected distance, the mutual Rydberg shift brings a particular dressed two-atom state into resonance with the ground manifold, producing a strong energy shift only within a narrow spatial window. Laser tuning moves the target distance to chosen neighbor shells and controls the peak strength and sharpness, without sub-wavelength positioning. Simulations confirm robust distance selectivity under realistic decoherence, and we also identify genuine three-body resonance features that enable higher-order connectivity. Applications include parallel entangling operations with global pulses (measurement-based quantum computing), faster syndrome extraction in surface-code layouts, and quantum simulation with customizable interaction graphs. 

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