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