Efficient and high-fidelity entanglement in cavity QED without high cooperativity

The so-called state-carving protocol generates high-fidelity entangled states at an atom-cavity interface without requiring high cavity cooperativity. However, this protocol is limited to 50\% efficiency, which restricts its applicability. We propose a simple modification to the state-carving protocol to achieve efficient entanglement generation, with unit probability in principle. Unlike previous two-photon schemes, ours employs only one photon which interacts with the atoms twice - avoiding separate photon detections which causes irrecoverable probability loss. We present a detailed description and performance evaluation of our protocol under non-ideal conditions. High fidelity of 0.999 can be achieved with cavity cooperativity of only 34. Efficient state-carving paves the way for large-scale entanglement generation at cavity-interfaces for modular quantum computing, quantum repeaters and creating arbitrary shaped atomic graph states, essential for one-way quantum computing.