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We study number-phase uncertainty in a laser-driven, effectively four-levelatomic system under electromagnetically induced transparency (EIT) and coherentpopulation trapping (CPT). Uncertainty is described using (entropic) knowledgeof the two complementary variables, namely, number and phase, where knowledgeis defined as the relative entropy with respect to a uniform distribution. Inthe regime where the coupling and probe lasers are approximately of equalstrength, and the atom exists in a CPT state, there is coherence between theground states, and correspondingly large phase knowledge and lower numberknowledge. The situation is the opposite in the case where coupling laser ismuch stronger and the atom exists in an EIT state. We study these effects alsoin the presence of a higher-order nonlinear absorption, which is seen toproduce a dephasing effect.

An information theoretic study of number-phase complementarity in a four level atomic system