Abstract of PhD project In this work we study a new type of Fabry-Perot (FP) microcavity and its coupling with single quantum emitters at low temperature. The cavity consists of a curved micromirror machined with focused ion beam (FIB) and a planar distributed Bragg reflector. It has a combination of novel properties. The state-of-the-art FIB technology enables machining of micromirrors with radii of curvature smaller than 5 μm, and with large solid angle up to π. This combination is specific, in a way that it allows to operate a cavity at short cavity length and small mirror radius at the same time. This in total results in a mode volume smaller than 1 μm^3. Also, the open cavity geometry provides access for coupling with different families of emitters and gives easy tunability of cavity resonance and spatial mode matching.