Quantum correlations and quantum fisher information for a pair of superconducting qubits interacting with a quantized field under time-varying coupling

We propose a quantum model involving two superconducting qubits (SQs) interacting with a single-mode microwave cavity, influenced by a Kerr nonlinear medium and Ising interaction, within the framework of time-varying coupling (T-VC). The Hamiltonian of the system is determined, and we compute the density operator for both the full system and its subsystems. Physically, the Kerr medium introduces nonlinearity while the Ising interaction between SQs facilitates tunable SQs coupling. The interplay of these mechanisms allows for fine-tuned quantum control, crucial for maintaining coherence and managing decoherence processes. We examine the time evolution of key quantum properties, including SQ–SQ entanglement, SQs–cat field entanglement, and quantum Fisher information, as functions of system parameters. Finally, we investigate the dynamic relationships among these quantum measures, revealing mechanisms that can maximize entanglement and coherence under various parameter regimes.