A quantum field theoretic formulation of atom-boson interactions

The results from the application of quantum field theoretic techniques to a number of problems in quantum optics are presented. We firstly evaluate the relative convenience of three possible mappings of spin operators to fermion operators that enable the usual Feynman diagram approach to be used. These were the drone, quasi-spin and iso-spin mappings which were compared by applying each to an analysis of the coupled spin-phonon modes problem. Using the iso-spin mapping we derive methods useful in applications to ionic level systems. These are then used to develop diagram formulations of: the single-ion absorption spectrum, absorption pair spectra and single-ion Raman spectra. The present work on the single-ion absorption spectrum extends the results of previous workers while the pair spectrum formalism is a new approach enabling a straightforward analysis of Kramers ion pairs to be presented. The formalism for Raman scattering is applicable to both time-dependent and steady-state situations and also to both the near-resonant and for far from resonant regimes