  We have realized a fiber-based Fabry-Perot cavity with CO2 laser-machined
mirrors. It combines very small size, high finesse F>=130000, small waist and
mode volume, and good mode matching between the fiber and cavity modes. This
combination of features is a major advance for cavity quantum electrodynamics
(CQED), as shown in recent CQED experiments with Bose-Einstein condensates
enabled by this cavity [Y. Colombe et al., Nature 450, 272 (2007)]. It should
also be suitable for a wide range of other applications, including coupling to
solid-state emitters, gas detection at the single-particle level, fiber-coupled
single-photon sources and high-resolution optical filters with large stopband.
