Cryogenic platform for coupling color centers in diamond membranes to a fiber-based microcavity

We operate a fiber-based cavity with an inserted diamond membrane containing ensembles of silicon vacancy centers (SiV$^{-}$) at cryogenic temperatures ≥4 K. The setup, sample fabrication and spectroscopic characterization are described, together with a demonstration of the cavity influence by the Purcell effect. This paves the way towards solid-state qubits coupled to optical interfaces as long-lived quantum memories.