Theory of Quantum Gap Solitons
In analogy to an electronic band gap in semiconductor crystals, periodic dielectric structures have a photonic band gap, namely, a band of frequencies over which electromagnetic waves cannot propagate in any direction. Such structures are now known as photonic crystals. A photonic hand gap occurs due to destructive interference between waves scattered from the periodic dielectric structure. Hy nature any dielectric material is nonlinear. The nonlinearity changes photonic hand-gap properties to some degree. In one-dimensional (1D) photonic crystals, even weak nonlinearity acts as a large perturbation on these properties. In recent years it has been shown that 1D Kerr-nonlinear photonic crystals admit, hand-gap solitary waves, which are called gap solitons. Current studies correspond to classical gap solitons. Since quantum many-body properties of light can be important in nonlinear optical processes, we have developed the quantum theory of gap solitons in a 1D Kerr-nonlinear photonic crystal.