Optimizing Quantum Fisher Information for Quantum Metrology

Recent advances in quantum control have enabled the creation of entangled atomic states that surpass the standard quantum limit (SQL) and approach Heisenberg-limited precision. This work presents a practical scheme for generating spin-squeezed states, Dicke states, and their superpositions using engineered atom–atom interactions governed by the one-axis twisting (OAT) Hamiltonian. By leveraging the structure of the OAT energy spectrum and implementing optimized collective rotations, a rapid adiabatic passage protocol is developed to prepare metrologically useful entangled states with high fidelity. The performance of these states is quantified using quantum Fisher information (QFI), which determines the fundamental precision bound for parameter estimation. The proposed approach facilitates the generation of Dicke-like states with near-maximal QFI and enhanced robustness to variations in driving fields. Furthermore, the protocol demonstrates favorable time scaling for ensembles of up to approximately 10⁴ atoms, indicating its promise for next-generation quantum sensors operating at or near the Heisenberg limit.