  We show that a set of N identical qubits coupled to a single cavity resonator
can be decomposed into a set of independent subsystems, which can be thought of
as higher pseudospin generalisations of the Jaynes-Cummings model. We derive
and analyse the solutions to the equations of motion and demonstrate unusual
beating behaviour resulting from a new form of square-root-n-type non-linearity
appearing within a pseudospin ladder. Furthermore, we propose a relative phase
shift transformation which allows one to switch/initiate the multi-qubit state
in a desired pseudospin configuration, and show how such transformations can be
used to undo spontaneous single qubit decay. We discuss the conditions which
justify the validity of the rotating wave approximation in an N-qubit system.
