High Jaynes-Cummings pseudospins eigenstates in the homogeneous Tavis-Cummings model

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.