Quantum behavior of a many photons cavity field revealed by quantum discord

We investigate the quantum-to-classical crossover of a dissipative optical cavity mode based on measurement of the correlations between two atoms which do not interact with each other, but interact with the cavity mode. Firstly, we note that there is a time window where the mode has a classical behavior, which depends on the cavity decay rate, the atom-field coupling strength and the number of atoms. Then, considering only two atoms inside the cavity and working in the steady state of the system, we note that the entanglement between the atoms disappears with the increasing the mean number of photons of the cavity field (n). However, the quantum discord reaches an asymptotic non-zero value, even in the limit of n\rightarrow \infty. This happens either by increasing n coherently (applying a coherent driving field) or incoherently (raising the temperature of the reservoir coupled to the cavity mode). Therefore, the cavity mode, which is quantum by construction, always preserves its quantum behavior in the asymptotic limit and this is revealed only by the quantum discord.