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Analytic solutions for the spatial character and coherence properties of light scattered from two dipole-coupled atoms

Analytic solutions for steady-state expectation values of atomic quantities and second order correlations are obtained for a fully quantum treatment of two stationary dipole-coupled atoms driven in a standard geometric configuration by a near resonant laser. Explicit expressions for the spatial and coherence properties of the far-field scattered light intensity are derived, valid for the full range of system parameters. A comprehensive survey of the steady-state scattering behaviour is given, with key features precisely characterised, including subradiant scattering, and the regime in which the dipole-dipole coupling has significant effect. A regime is also found where the incoherent scattered light develops spatial interference fringes. We examine in detail a decorrelation approximation that has potential application for larger systems of atoms that are intractable in a full quantum treatment. Finally, we introduce the concept of an effective driving field and show that it can provide a direct and intuitive physical interpretation of key aspects of the system behaviour, including subradiant scattering.