Giant Cooperative Lamb Shift in a density-modulated slab of two-level atoms

A 'slab' of two-level atoms prepared in a superradiant Dicke state exhibits interesting enhancement of the Cooperative Decay Rate (CDR) when its density is modulated at the Bragg condition. In this Letter, complete analytical formulas are given, not only for CDR but also for the Cooperative Lamb Shift (CLS), both at and near the Bragg condition, as a function of the depth of modulation, the thickness of the slab, and the detuning from the Bragg condition. A major new result is that for detuning O(1/m) (where m=thickness/wavelength) the CLS takes on 'giant' values, proportional to m. The reason for this giant CLS is explored.