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In recent years there has been rapid progress into realising a working universal quantum computer, in particular with the development of chip-based radio frequency ion traps. The next significant leap will come with successfully integrating optical cavities into these ion traps to allow for interaction between remote ions via photons as required for more efficient and scalable quantum networking schemes. Fibre-tip cavities are especially interesting for such applications as they enable highly efficient coupling of photons from the cavity into optical fibres for onward transmission.
Here we analyse theoretically and numerically the effects of parallel off-axial misalignment in millimetre scale optical Fabry-Perot cavities. While near-concentric cavity configurations produce the smallest mode waist and thus strongest coupling to a trapped ion, their mode is extremely sensitive to misalignment. Shorter cavities exhibit more robust modes, but at the cost of larger mode waists. For example, for typical experimental parameters (mirror radius of curvature 0.7 mm, mirror diameter 0.140 mm, operation wavelength 850 nm) we find that the cavity lifetime is reduced by a factor 1/e for a misalignment of 0.95 nm for a beam waist of 2.91 um (cavity length of 1.397 mm), which increases to 11.0 nm for a waist of 4.33 um (length of 1.386 mm), and 3.12 um for a waist of 7.38 um (length of 1.273 mm). In the parameter regimes of interest, we derive a simple relation between cavity length, mirror radius, and misalignment sensitivity. Finally, we also consider the effect of mode matching of the misaligned cavity mode with the optical mode of the fibre for efficient cavity to fibre coupling.
In conclusion, our model allows us to optimise photon-ion coupling in fibre-tip resonators for quantum information processing in the presence of finite fabrication and alignment tolerances.
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