Modulation and protection of entanglement in a two-qubit system via two interacting oscillator control

We investigate the control and protection of two-qubit entanglement through engineered interactions between two auxiliary harmonic oscillators. Each qubit is coupled to a local oscillator via a dephasing interaction, while the oscillators interact through independently tunable position-position and momentum-momentum couplings. Employing the characteristic-function representation, we obtain analytical solutions for the composite-system dynamics and examine how the stability properties of the coupled oscillators determine the evolution of two-qubit concurrence. Our analysis reveals distinct dynamical regimes exhibiting entanglement revivals, suppression, or decay, and identifies configurations in which oscillator interactions effectively reduce entanglement degradation. We further investigate the influence of thermal dissipation using local and global master-equation descriptions, demonstrating that suitable oscillator couplings can preserve substantial two-qubit entanglement under the dissipative conditions considered. These results establish a connection between the dynamical stability of auxiliary bosonic modes and the controllability of entanglement in discrete-variable quantum systems, providing a potential strategy for entanglement protection through engineered oscillator interactions.