Entanglement and Coherence in Qutrits-Field Systems: Periodic Behavior under Parity Deformation and Time-Varying Coupling

In this manuscript, we consider an extension of harmonic oscillator systems that uses parity concept to develop the quantum model for a qutrits-field system (Qs-FS), based on a particular Heisenberg algebraic deformation. We introduce a quantum framework for a two Qs interacting with a cavity field, where the field is initially set in parity-deformed coherent states (P-DCSs). We examine the dynamical features of this quantum system considering the effects of both the time-varying coupling (T-VC) and deformation parameter. Our study focuses on the entanglement within the Qs-F state and the Q-Q state, as well as the Qs coherence. Our findings indicate that the system exhibits periodic occurrences of maximum entanglement and coherence throughout its dynamical evolution. Additionally, we explore how the T-VC and deformation influence the statistical properties of the quantized field during the time evolution.