Theory of two-atom coherence in gases. I. Master equations

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Abstract
The response of a collision-broadened gas sample to driving coherent radiation is studied theoretically, taking into account effects of coherent excitations of two or more atoms (or molecules). In analogy to the Bloch-type master equation for one-atom coherences, describing the motion of a single atom "dressed" by the relevant (incident and detected) field modes, a master equation is derived for two-atom coherences, including an effective interaction of the Bethe-Salpeter—type, accounting for the mutual interaction of the coherently driven pair. The master equation includes also all symmetrization effects owing to resonance exchange between identical atoms, and is limited to nonreactive gas atoms (or molecules) undergoing binary collisions, including otherwise all (internal and translational) relaxation effects. The self-energy kernels are expressed in a nonperturbative fashion, in terms of binary-collision scattering amplitudes, and include renormalization effects due to coincidence of radiative couplings with the collisions (optical and radiative collisions). The concept of two-atom coherences is generalized to higher coherence ranks by constructing a hierarchy of master equations, including vertex operators that upgrade or downgrade the coherence rank, as a prelude to a diagrammatic method for calculating continuous-wave spectra. This hierarchy is compared with prevalent Agarwal-type master equations, based on the Dicke pseudospin method, and used in the study of two-level atoms.