  We experimentally study a fiber-based three-stage nonlinear interferometer
and demonstrate its application in generating heralded single photons with high
efficiency and purity by spectral engineering. We obtain a heralding efficiency
of 90% at a brightness of 0.039 photons/pulse. The purity of the source is
checked by two-photon Hong-Ou-Mandel interference with a visibility of 95%+-6%
(after correcting Raman scattering and multi-pair events). Our investigation
indicates that the heralded source of single photons produced by the
three-stage nonlinear interferometer has the advantages of high purity, high
heralding efficiency, high brightness, and flexibility in wavelength and
bandwidth selection.
