  We study number-phase uncertainty in a laser-driven, effectively four-level
atomic system under electromagnetically induced transparency (EIT) and coherent
population trapping (CPT). Uncertainty is described using (entropic) knowledge
of the two complementary variables, namely, number and phase, where knowledge
is defined as the relative entropy with respect to a uniform distribution. In
the regime where the coupling and probe lasers are approximately of equal
strength, and the atom exists in a CPT state, there is coherence between the
ground states, and correspondingly large phase knowledge and lower number
knowledge. The situation is the opposite in the case where coupling laser is
much stronger and the atom exists in an EIT state. We study these effects also
in the presence of a higher-order nonlinear absorption, which is seen to
produce a dephasing effect.
