  We propose to use chirped pulses propagating near a bandgap to remotely
address quantum emitters. We introduce a particular family of chirped pulses
that dynamically self-compress to sub-wavelength spot sizes during their
evolution in a medium with a quadratic dispersion relation. We analytically
describe how the compression distance and width of the pulse can be tuned
through its initial parameters. We show that the interaction of such pulses
with a quantum emitter is highly sensitive to its position due to effective
Landau-Zener processes induced by the pulse chirping. Our results propose pulse
engineering as a powerful control and probing tool in the field of quantum
emitters coupled to structured reservoirs.
