  Interference and coincidence detection of two photons emitted by two remote
ions can lead to an entangled state which is a critical resource for scalable
quantum information processing. Currently, the success probabilities of
experimental realizations of this protocol are mainly limited by low coupling
efficiency of a photon emitted by an ion into a single mode fiber. Here, we
consider two strategies to enhance the collection probability of a photon
emitted from a trapped Yb ion, using analytic methods that can be easily
applied to other types of ion or neutral atoms. Our analysis shows that we can
achieve fiber coupling efficiency of over 30% with an optical cavity made of a
flat fiber tip and a spherical mirror. We also investigate ways to increase the
fiber coupling efficiency using high numerical aperture optics, and show that
collection probability of over 15% is possible with proper control of
aberration.
