We examine the quantum dynamics of entanglement and quantum Fisher information in a three-level atom (T–LA) interacting with a parity-deformed field (PDF) within the Heisenberg algebra framework. Utilizing the parity extension of harmonic oscillators, we describe the PDF through coherent states and formulate a detailed quantum model for the T–LA-PDF system, incorporating both time-dependent and time-independent coupling regimes. We explore the cascade (Ξ) and lambda (Λ) configurations of the T–LA, emphasizing the temporal evolution of essential quantum quantifiers, including T–LA populations, T–LA-PDF entanglement, and quantum Fisher information. Our results demonstrate that the interaction among field nonlinearity, coupling dynamics, and T–LA configuration facilitates accurate control and modulation of these quantifiers throughout the evolution.
Algarni et al. (Fri,) studied this question.