Relation between atomic coherent-state representation, state multipoles, and generalized phase-space distributions

The relationship between the atomic coherent-state representation of Arecchi et al. Phys. Rev. A 6, 2211 (1972) and the state multipoles is established. The state multipoles are used to develop a theory of generalized phase-space distributions for angular momentum (collective atomic) systems. The general theory for angular momentum systems is shown to have many features in common with the general theory for boson systems Phys. Rev. D 2, 2161 (1970). These generalized phase-space distributions contain as a special case the coherent-state representation of Arecchi et al. The applications of the generalized phase-space distributions and state multipoles to the dynamical problems and to the calculation of multitime correlations are given. State-multipole techniques are used to give a brief discussion of the master equation describing cooperative resonance fluorescence.