  We perform balanced homodyne detection of the electromagnetic field in a
single-mode tapered optical nanofiber surrounded by rubidium atoms in a
magneto-optical trap. Resonant fluorescence of atoms into the nanofiber mode
manifests itself as increased quantum noise of the field quadratures. The
autocorrelation function of the homodyne detector's output photocurrent
exhibits exponential fall-off with a decay time constant of $26.3\pm 0.6$ ns,
which is consistent with the theoretical expectation under our experimental
conditions. To our knowledge, this is the first experiment in which
fluorescence has been observed and measured by balanced optical homodyne
detection.
