  The strong non-linear optical response of atomic systems in
electromagnetically induced transparency (EIT) states is considered as a means
to detect the presence of small perturbations to steady states. For the 3-level
system, expressions for the group velocity and group velocity dispersion (GVD)
were derived and a quantum control protocol was established to account for the
change in the chirp spectrum of a probe pulse when the steady state was
perturbed. This was applied to the propagation of slow Cherenkov polaritons in
the medium due to the passage of a train of high-energy charged particles (high
energy particles). The choice of the initial steady state with focus on the
slow light condition and strong narrowly confined dispersion, equated to the
continuous trapping of Cherenkov polaritons in the medium along a narrow group
cone, allowing for non-trivial fields to accumulate. Considering another medium
prepared for the detection of the radiation, sweeping of the control field and
detuning parameters in the field-atom parameter space showed the presence of
optimal regions to maximize the first order perturbation in the coherences
creating changes in the optical responses that modify the chirp spectra of
probe pulses.
