Quantum optics of two-level atoms in a dielectric: comparison of macroscopic and microscopic quantizations of the dielectric

Abstract We obtain Langevin–Bloch equations of motion for optically resonant atoms embedded in a dielectric host using both the conventional macroscopic quantization of the field in a dielectric and the microscopic quantization of the Lorentz model of enumerated oscillators embedded in the vacuum. The two sets of equations of motion exhibit substantial differences in their dependence on the index of refraction of the host dielectric medium. We compare and contrast the essential conceptual features of the macroscopic and microscopic theories, relating the inconsistency of the results to differences in the underlying Maxwellian and Lorentzian descriptions of the interaction of the radiation with the vacuum and matter. We invoke the correspondence principle to discriminate between the two results and demonstrate that quantization of the macroscopic Maxwell equations leads to incorrect equations of motion for embedded two-level atoms while the microscopic result is consistent with the correspondence principle.

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