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

TL;DR

This paper investigates the quantum uncertainty between number and phase in a four-level atomic system under EIT and CPT conditions, revealing how laser strengths influence coherence and knowledge distribution, including effects of nonlinear absorption.

Contribution

It provides a novel entropic knowledge-based analysis of number-phase complementarity in a four-level atomic system under different quantum states and nonlinear effects.

Findings

Large phase knowledge in CPT states with equal laser strengths

Lower number knowledge in CPT states compared to EIT states

Nonlinear absorption induces dephasing effects

Abstract

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.