Time-bin entanglement in the deterministic generation of linear photonic cluster states

We theoretically investigate strategies for the deterministic creation of trains of time-bin entangled photons using an individual quantum emitter described by a $\Lambda$-type electronic system. We explicitly demonstrate the theoretical generation of linear cluster states with substantial numbers of entangled photonic qubits in full microscopic numerical simulations. The underlying scheme is based on the manipulation of ground state coherences through precise optical driving. One important finding is that the most easily accessible quality metrics, the achievable rotation fidelities, fall short in assessing the actual quantum correlations of the emitted photons in the face of losses. To address this, we explicitly calculate stabilizer generator expectation values as a superior gauge for the quantum properties of the generated many-photon state. With widespread applicability also to other emitter and excitation-emission schemes, our work lays the conceptual foundations for an in-depth practical analysis of time-bin entanglement based on full numerical simulations with predictive capabilities for realistic systems and setups including losses and imperfections. The specific results shown in the present work illustrate that with controlled minimization of losses and realistic system parameters for quantum-dot type systems, useful linear cluster states of significant lengths can be generated in the calculations, discussing the possibility of scalability for quantum information processing endeavors.