  Atomic frequency comb (AFC) quantum memory is a favorable protocol in long
distance quantum communication. Putting the AFC inside an asymmetric optical
cavity enhances the storage efficiency but makes the measurement of the comb
properties challenging. We develop a theoretical model for cavity-enhanced AFC
quantum memory that includes the effects of dispersion, and show a close
alignment of the model with our own experimental results. Providing semi
quantitative agreement for estimating the efficiency and a good description of
how the efficiency changes as a function of detuning, it also captures certain
qualitative features of the experimental reflectivity. For comparison, we show
that a theoretical model without dispersion fails dramatically to predict the
correct efficiencies. Our model is a step forward to accurately estimating the
created comb properties, such as the optical depth inside the cavity, and so
being able to make precise predictions of the performance of the prepared
cavity-enhanced AFC quantum memory.
