Entanglement detection via quantum Fisher information in a coupled atom-field system

We consider a system of finite number of particles collectively interacting with a single mode coherent field inside the cavity. Depending on the strength of the initial field compared to the number of atoms, we introduce three regimes of weak, intermediate and strong field interaction. The dynamics of multi-particle entanglement detected by quantum Fisher information is studied in each regime. Specifically, for the two extreme limits of weak and strong field regimes, analytical results are found. Moreover, we have compared our outcomes with spin squeezing. It is seen that in the weak field regime, spin squeezing and quantum Fisher information coincides. However, by increasing the initial field population toward the strong field regime, spin squeezing compared to quantum Fisher information gradually decreases and eventually fails in detecting entanglement. In addition, in the two-atom system, we also consider concurrence. In this case, the quantum Fisher information and concurrence show good agreement in predicting entanglement peaks.