Using the strong dispersive coupling to a high-cooperativity cavity, we demonstrate fast and nondestructive number-resolved detection of atoms in optical tweezers. We observe individual atom-atom collisions, quantum state jumps, and atom loss events with a time resolution of $100\mathrm{\mu }\mathrm{s}$ through continuous measurement of cavity transmission. Using adaptive feedback control in combination with the nondestructive measurements, we further prepare a single atom with 92(2)% probability.

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• Cavity quantum electrodynamics
• Cooling & trapping
• Interatomic & molecular potentials
• Optical pumping
• Quantum control
• Ultracold collisions