Efficient recycling strategies for preparing large Fock states from single-photon sources --- Applications to quantum metrology

Fock states are a fundamental resource for many quantum technologies such as quantum metrology. While much progress has been made in single-photon source technologies, preparing Fock states with large photon number remains challenging. We present and analyze a bootstrapped approach for non-deterministically preparing large photon-number Fock states by iteratively fusing smaller Fock states on a beamsplitter. We show that by employing state recycling we are able to exponentially improve the preparation rate over conventional schemes, allowing the efficient preparation of large Fock states. The scheme requires single-photon sources, beamsplitters, number-resolved photo-detectors, fast-feedforward, and an optical quantum memory.