1. K. Cho, Optical Response of Nanostructures: Microscopic Nonlocal Theory (Springer-Verlag, Heidelberg, 2003), Chap. 4 and 5.
2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, Cambridge, 1995), Chap. 15.
3. Two-photon nonlinearity in general cavity QED systems
4. A familiar expression of a coherent state is |μ 〉 = 𝒩 exp(μc†)|0〉 (single-mode notation). By replacing the single-mode operator c† with ∫ dr f (r)c̃†r, the multimode notation of Eq. (5) is obtained.
5. Such a system can be realized in the weak coupling (κ ≫ g) and dissipationless (ν → 0) limit of a cavity QED system. The atomic decay rate is then given by Γ = 4g2/κ.