This paper presents a high-fidelity remote entanglement protocol for trapped atomic qubits using time-bin encoded photons. The protocol enables entanglement between two remote trapped ions, each in separate vacuum chambers, through the timing of emitted photons. The fidelity of the entangled state was measured to be 97.0(4), demonstrating the feasibility of achieving fidelities beyond 99.9%. The protocol uses time-bin encoding, which is less sensitive to polarization errors and allows for long-distance quantum communication. The entanglement is achieved through a measurement-based error detection process and suppression of atomic recoil errors. The protocol involves generating time-bin encoded photons from the ions, interfering them, and detecting them to herald the entanglement of the ion memories. The fidelity is further improved by erasing erasure errors from the atomic qubits with minimal overhead. The protocol is scalable to high-dimensional quantum memories and enables long-distance quantum communication between quantum nodes. The results demonstrate that time-bin encoded photons can achieve high-fidelity entanglement, making them a promising candidate for scalable quantum networks and modular quantum computers. The study also addresses timing and atomic recoil errors, which are critical for maintaining high fidelity in the entanglement process. The results show that the fidelity limits for remote entanglement based on photons can be better than 0.999, enabling the modular scaling of quantum computers based on atomic qubits and long-distance quantum communication. The protocol is supported by experimental data and theoretical models, and the results are consistent with previous studies in the field of quantum information processing.This paper presents a high-fidelity remote entanglement protocol for trapped atomic qubits using time-bin encoded photons. The protocol enables entanglement between two remote trapped ions, each in separate vacuum chambers, through the timing of emitted photons. The fidelity of the entangled state was measured to be 97.0(4), demonstrating the feasibility of achieving fidelities beyond 99.9%. The protocol uses time-bin encoding, which is less sensitive to polarization errors and allows for long-distance quantum communication. The entanglement is achieved through a measurement-based error detection process and suppression of atomic recoil errors. The protocol involves generating time-bin encoded photons from the ions, interfering them, and detecting them to herald the entanglement of the ion memories. The fidelity is further improved by erasing erasure errors from the atomic qubits with minimal overhead. The protocol is scalable to high-dimensional quantum memories and enables long-distance quantum communication between quantum nodes. The results demonstrate that time-bin encoded photons can achieve high-fidelity entanglement, making them a promising candidate for scalable quantum networks and modular quantum computers. The study also addresses timing and atomic recoil errors, which are critical for maintaining high fidelity in the entanglement process. The results show that the fidelity limits for remote entanglement based on photons can be better than 0.999, enabling the modular scaling of quantum computers based on atomic qubits and long-distance quantum communication. The protocol is supported by experimental data and theoretical models, and the results are consistent with previous studies in the field of quantum information processing.