Post-Selection Free Generation of Multi-Photon Added Coherent States

Non-Gaussian quantum states are essential resources for continuous-variable quantum information processing and for metrology. Among these, multi-photon added coherent states bridge classical and non-classical behaviors; however, their generation typically relies on small photon numbers and probabilistic heralding schemes. Here, we propose a protocol for the post-selection free generation of high fidelity multi-photon added coherent states using the photon blockade effect in a driven Kerr nonlinear resonator, where such states emerge naturally during the dynamics. We demonstrate that high-fidelity states can be prepared by optimizing the external drive power and the interaction time. Furthermore, we show that the protocol is robust under realistic experimental conditions, achieving fidelities of $\approx 99\%$ with current state-of-the-art parameters. Our results unlock a deterministic route to complex non-classical states using well-established quantum optical platforms.