  In recent years the interest in studying interactions of Rydberg atoms or
ensembles thereof with optical and microwave frequency fields has steadily
increased, both in the context of basic research and for potential applications
in quantum information processing. We present measurements of the dispersive
interaction between an ensemble of helium atoms in the 37s Rydberg state and a
single resonator mode by extracting the amplitude and phase change of a weak
microwave probe tone transmitted through the cavity. The results are in
quantitative agreement with predictions made on the basis of the dispersive
Tavis-Cummings Hamiltonian. We study this system with the goal of realizing a
hybrid between superconducting circuits and Rydberg atoms. We measure maximal
collective coupling strengths of 1 MHz, corresponding to 3*10^3 Rydberg atoms
coupled to the cavity. As expected, the dispersive shift is found to be
inversely proportional to the atom-cavity detuning and proportional to the
number of Rydberg atoms. This possibility of measuring the number of Rydberg
atoms in a nondestructive manner is relevant for quantitatively evaluating
scattering cross sections in experiments with Rydberg atoms.
