  Development of the optical frequency comb has revolutionised metrology and
precision spectroscopy due to its ability to provide a precise and direct link
between microwave and optical frequencies. A novel application of frequency
comb technology that leverages both the ultrashort duration of each laser pulse
and the exquisite phase coherence of a train of pulses is the generation of
frequency combs in the extreme ultraviolet (XUV) via high harmonic generation
(HHG) in a femtosecond enhancement cavity. Until now, this method has lacked
sufficient average power for applications, which has also hampered efforts to
observe phase coherence of the high-repetition rate pulse train produced in the
extremely nonlinear HHG process. Hence, the existence of a frequency comb in
the XUV has not been confirmed. We have overcome both challenges. Here, we
present generation of >200 {\mu}W per harmonic reaching 50 nm, and the
observation of single-photon spectroscopy signals for both an argon transition
at 82 nm and a neon transition at 63 nm. The absolute frequency of the argon
transition has been determined via direct frequency comb spectroscopy. The
resolved 10-MHz linewidth of the transition, limited by the transverse
temperature of the argon atoms, is unprecedented in this spectral region and
places a stringent upper limit on the linewidth of individual comb teeth. Due
to the lack of cw lasers, these frequency combs are currently the only
promising avenue towards extending ultrahigh precision spectroscopy to below
the 100-nm spectral region with a wide range of applications that include
spectroscopy of electronic transitions in molecules, experimental tests of
bound state and many body quantum electrodynamics in He+ and He, development of
next-generation "nuclear" clocks, and searches for spatial and temporal
variation of fundamental constants using the enhanced sensitivity of highly
charged ions.
