Bi- and uni-photon entanglement in two-way cascaded fiber-coupled atom–cavity systems

•Quantum jump approach to two-photon entanglement in two-way cascaded cavity systems.•Weak coupling supporting two-photon entanglement more than the strong coupling.•Hybrid atom–cavity entanglement posing an upper bound on atom–atom entanglement.•At least two cavity decay times needed to entangle atom–cavity systems.•Rabi oscillations not affecting the entanglement between atom–cavity systems.

We theoretically investigate the two-photon entanglement in fiber-coupled, two-way cascaded atom–cavity systems. In particular, we demonstrate that, it is possible to generate two-photon entanglement in both weak coupling (atom–cavity coupling rate |g||g| smaller than the cavity leakage rate κ  ) and strong coupling regimes (κ<|g|κ<|g|) in this system, when both atoms start off in an excited state. By employing the quantum trajectory method, we characterize the two-photon entanglement in terms of von-Neumann entropy and show that the amount of entanglement exceed considerably (almost double) when κ>|g|κ>|g|. We also quantified the amount of entanglement when instead of two excitations there is a single excitation in the system in the beginning.