Ultimate bound and optimal measurement for estimation of coupling constant in Tavis–Cummings model

We seek to study the problem of estimating the atoms-field coupling constant in Tavis–Cummings model for interaction between two atoms and an electromagnetic field by means of local estimation theory. We calculate the quantum Fisher information (QFI) for the most general pure probe state that undergoes evolution generated by the Hamiltonian of the Tavis–Cummings model; then, proper probe states which maximize the QFI are determined. Furthermore, we consider subspaces separately and show that QFI for atomic subspace (contains both qubits) and cavity field subspace can reach the maximum value of QFI in the whole space by choosing proper initial state. Finally, the optimal measurement that saturates the Cramer–Rao bound, i.e., the measurement with Fisher information equal to QFI, for considered states are determined in the whole space and the subspaces, separately.