Optical microscope and tapered fiber coupling apparatus for a dilution refrigerator

We have developed a system for tapered fiber measurements of optomechanical resonators inside a dilution refrigerator, which is compatible with both on- and off-chip devices. Our apparatus features full three-dimensional control of the taper-resonator coupling conditions enabling critical coupling, with an overall fiber transmission efficiency of up to 70%. Notably, our design incorporates an optical microscope system consisting of a coherent bundle of 37,000 optical fibers for real-time imaging of the experiment at a resolution of $\sim$1 $\mu$m. We present cryogenic optical and optomechanical measurements of resonators coupled to tapered fibers at temperatures as low as 9 mK.