  The ability to detect single photons with high efficiency is a crucial
requirement for various quantum information applications. By combining the
storage process of a quantum memory for photons with fluorescence-based quantum
state measurement, it is in principle possible to achieve high efficiency
photon counting in large ensembles of atoms. The large number of atoms can,
however, pose significant problems in terms of noise stemming from imperfect
initial state preparation and off-resonant fluorescence. We propose a concrete
implementation of a photon number resolving detector based on an ion Coulomb
crystal inside a moderately high-finesse optical cavity. The cavity enhancement
leads to an effective optical depth of 15 for a finesse of 3000 with only about
1500 ions interacting with the light field. We show that these values allow for
essentially noiseless detection with an efficiency larger than 90%. Moderate
experimental parameters allow for repetition rates of about 5 kHz, limited by
the time needed for fluorescence collection. Potential applications are
discussed.
