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.