A millikelvin all-fiber cavity optomechanical apparatus for merging with ultra-cold atoms in a hybrid quantum system

We describe the construction of an apparatus designed to realize a hybrid quantum system comprised of a cryogenically cooled mechanical oscillator and ultra-cold \(^{87}\)Rb atoms coupled via light. The outstanding feature of our instrument is an in-situ adjustable asymmetric all-fiber membrane-in-the-middle cavity located inside an ultra-high vacuum dilution refrigerator based cryostat. We show that Bose-Einstein condensates of \(N=2\times10^6\) atoms can be produced in less than 20 s and demonstrate a single photon optomechanical coupling strength of \(g_0=2\pi\times9\) kHz employing a high-stress Si\(_3\)N\(_4\) membrane with a mechanical quality factor \(Q_{\rm m}>10^7\) at a cavity set-up temperature of \(T_{\rm MiM}=480\) mK.