Nondestructive Rydberg atom counting with mesoscopic fields in a cavity

We present an efficient, state-selective, nondemolition atom-counting procedure based on the dispersive interaction of a sample of circular Rydberg atoms with a mesoscopic field contained in a high-quality superconducting cavity. The state-dependent atomic index of refraction, proportional to the atom number, shifts the classical field phase. A homodyne procedure translates the information from the phase to the intensity. The final field intensity is readout by a mesoscopic atomic sample. This method opens promising routes for quantum information processing and nonclassical state generation with Rydberg atoms.