Estimation theory of photon-magnon coupling strength in a driven-dissipative double-cavity-magnon system

Cavity-magnon systems are emerging as a fruitful architecture for the integration of quantum technologies and spintronic technologies, where magnons are coupled to microwave photons via the magnetic-dipole interaction. Controllable, the photon-magnon (P-M) couplings provide a powerful means of accessing and manipulating quantum states in such hybrid systems. Thus, determining the relevant P-M couplings is a fundamental task. Here we address the quantum estimation problem for the P-M coupling strength in a double-cavity-magnon system with drive and dissipation. The effects of various physical factors on the estimation precision are investigated and the underlying physical mechanisms are discussed in detail. Considering that in practical experiments it is almost infeasible to perform measurements on the global quantum state of this composite system, we identify the optimal subsystem for performing measurements and estimations. Further, we evaluate the performance of different Gaussian measurements, indicating that optimal Gaussian measurement almost saturates the ultimate theoretical bound on the estimation precision given by the quantum Fisher information.