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We study the nonlinear dynamics of an ensemble of cold trapped atoms with ahyperfine transition magnetically coupled to a resonant microwave cavity mode.Despite the minute single atom coupling one obtains strong coupling betweencollective hyperfine qubits and microwave photons enabling coherent transfer ofan excitation between the long lived atomic qubit state and the mode. Evidenceof strong coupling can be obtained from the cavity transmission spectrum evenat finite thermal photon number. The system makes it possible to study furtherprominent collective phenomena such as superradiant decay of an invertedensemble or the building of a narrowband stripline micromaser locked to anatomic hyperfine transition.

Cavity QED with an ultracold ensemble on a chip: prospects for strong magnetic coupling at finite temperatures