  We observe a sixfold Purcell broadening of the D$_2$ line of an optically
trapped $^{87}\text{Rb}$ atom strongly coupled to a fiber cavity. Under
external illumination by a near-resonant laser, up to $90\%$ of the atom's
fluorescence is emitted into the resonant cavity mode. The sub-Poissonian
statistics of the cavity output and the Purcell enhancement of the atomic decay
rate are confirmed by the observation of a strongly narrowed antibunching dip
in the photon autocorrelation function. The photon leakage through the
higher-transmission mirror of the single-sided resonator is the dominant
contribution to the field decay
($\kappa\!\approx\!2\pi\!\times\!50\,\text{MHz}$), thus offering a
high-bandwidth, fiber-coupled channel for photonic interfaces such as quantum
memories and single-photon sources.
