Towards a Realistic Model for Cavity-Enhanced Atomic Frequency Comb Quantum Memories: The Critical Role of Dispersion

Future quantum networks rely on long-distance quantum communication which is limited due to the unavoidable photon transmission loss in optical fibers. Quantum repeaters (QRs) are promising quantum alternatives to play the role of classical amplifiers. Atomic frequency comb (AFC) quantum memory implemented in rare-earth-ion doped crystals is a favorable protocol in long-distance quantum communication based on quantum repeaters. 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 and investigate the role of dispersion in the model. We demonstrate that including the effect of dispersion leads to a good agreement between experimental and model results, whereas the model without dispersion falls short strikingly. Most importantly, the model with dispersion provides a much closer quantitative agreement for estimating the efficiency and a drastically better description of how the efficiency changes as a function of detuning. Furthermore, it better captures certain qualitative features of the experimental reflectivity. Our model is a step forward to accurately estimating the created comb properties, such as the optical depth inside the cavity, and so to being able to make precise predictions of the performance of the prepared cavity-enhanced AFC quantum memory.