  The ability to detect the interaction of light and matter at the
single-particle level is becoming increasingly important for many areas of
science and technology. The absorption or emission of a photon on a narrow
transition of a trapped ion can be detected with near unit probability, thereby
enabling the realization of ultra-precise ion clocks and quantum information
processing applications. Extending this sensitivity to broad transitions is
challenging due to the difficulty of detecting the rapid photon scattering
events in this case. Here, we demonstrate a technique to detect the scattering
of a single photon on a broad optical transition with high sensitivity. Our
approach is to use an entangled state to amplify the tiny momentum kick an ion
receives upon scattering a photon. The method should find applications in
spectroscopy of atomic and molecular ions and quantum information processing.
