Scalable Generation of Macroscopic Fock States Exceeding 10,000 Photons

Abstract: The scalable preparation of bosonic quantum states with macroscopic excitations poses a fundamental challenge in quantum technologies, limited by control complexity and photon-loss rates that severely constrain prior theoretical and experimental efforts to merely dozens of excitations per mode. Here, based on the duality of the quantum state evolution in Fock state space and the optical wave-function propagation in a waveguide array, we introduce a Kerr-engineered multi-lens protocol in a single bosonic mode to deterministically generate Fock states exceeding $10,000$ photons. By optimizing phase and displacement operations across lens groups, our approach compensates for non-paraxial aberrations, achieving fidelities above $73\%$ in numerical simulations for photon numbers up to $N=100,000$. Counterintuitively, the protocol's execution time scales as $N^{-1/2}$ with the target photon number $N$, exhibiting robustness against the photon loss. Our framework enables exploration of quantum-to-classical transitions of giant Fock states, paving the way for advanced quantum metrology with significant quantum gains, and error-corrected quantum information processing in high-dimensional Hilbert spaces.