Metrology and correlation dynamics in a driven-dissipative cavity QED system accompanied with nonlinearities

The generation of robust, metrologically useful quantum states in realistic open systems is contingent on a complex interplay between coherent dynamics, control fields, and environmental decoherence. Through comprehensive numerical simulations of a driven-dissipative cavity QED system, we systematically explore this interplay and uncover a set of non-trivial design principles for engineering practical quantum advantage. Our central finding reveals a critical trade-off between a state’s theoretical complexity and its operational resilience: we consistently demonstrate that the simpler entanglement structure generated by One-Axis Twisting (OAT) is significantly more robust than the more complex, yet fragile, states produced by Two-Axis Twisting. Furthermore, we establish that physical effects typically considered detrimental can be harnessed as protocol-dependent stabilization resources. Strong optical nonlinearities can create protected manifolds that shield the OAT state from decoherence, while strong counter-rotating interactions–a signature of the ultrastrong coupling regime–can actively stiffen the quantum state against metrologically harmful phase-space rotations. These results culminate in a revised design paradigm for quantum technologies: achieving practical quantum advantage necessitates a holistic co-design of the initial entangled state, the control protocol, and the intrinsic physical characteristics of the platform itself.