Prospects for Generation and Measurement of Arbitrary Photon Fock States

The creation of arbitrary photon Fock states is an important step for various tasks of interest, from solving classically hard problems with linear optics quantum computing networks to creating NOON states that could perform metrology with enhanced resolution at the Heisenberg limit. Here we report on our progress in using a Rydberg-blockaded atomic ensemble to experimentally generate arbitrary photon Fock states. We will generate one Rydberg excitation at a time, then "shelve" the excitation into the ground-state manifold, storing it there while we repeat the process n times. The blockaded nature of the process allows us to do additional shelving while not "un-shelving" those already stored. We will read out all the excitations at once to generate an n-photon Fock state, and reconstruct the number distribution of our output state using click/no-click detectors and a version of the expectation-maximization algorithm, whose robustness to experimental imperfections we also study.