Although our approach to optimization can be applied to most operating regimes, here we consider cavities suitable for typical ion-trapping experiments and with substantial transverse misalignment of the mirrors. We show that in many relevant cases it is possible to approximately separate the geometric aspects of the cooperativity from those associated with the atomic system and the mirror surfaces themselves, greatly simplifying the optimization procedure. In this work, we present a systematic approach to this problem that offers a means to identify efficient and robust operating regimes and to elucidate the trade-offs involved in the design process, allowing engineering efforts to be focused on the most sensitive and critical parameters. In the design optimization of ion-cavity interfaces for quantum networking applications, difficulties occur due to the many competing figures of merit and highly interdependent design constraints, many of which present “soft limits,” which are amenable to improvement at the cost of engineering time.
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