  We describe a high-resolution spectroscopy method, in which the detection of
single excitation events is enhanced by a complete loss of coherence of a
superposition of two ground states. Thereby, transitions of a single isolated
atom nearly at rest are recorded efficiently with high signal-to-noise ratios.
Spectra display symmetric line shapes without stray-light background from
spectroscopy probes. We employ this method on a $^{25}$Mg$^+$ ion to measure
one, two, and three-photon transition frequencies from the 3S ground state to
the 3P, 3D, and 4P excited states, respectively. Our results are relevant for
astrophysics and searches for drifts of fundamental constants. Furthermore, the
method can be extended to other transitions, isotopes, and species. The
currently achieved fractional frequency uncertainty of $5 \times 10^{-9}$ is
not limited by the method.
