Cryogenic platform for coupling color centers in diamond membranes to a fiberbased microcavity.

We operate a fiberbased cavity with an inserted diamond membrane containing ensembles of silicon vacancy centers (SiV$^-$) at cryogenic temperatures $ \geq4~$K. The setup, sample fabrication and spectroscopic characterization is 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.