  Infrared and visible light beams carrying orbital angular momentum (OAM) are
currently thoroughly studied for their extremely broad applicative prospects,
among which are quantum information, micromachining and diagnostic tools. Here
we extend these prospects, presenting a comprehensive study for the synthesis
and full characterization of optical vortices carrying OAM in the extreme
ultraviolet (XUV) domain. We confirm the upconversion rules of a femtosecond
infrared helically phased beam into its high-order harmonics, showing that each
harmonic order carries the total number of OAM units absorbed in the process up
to very high orders (57). This allows us to synthesize and characterize
helically shaped XUV trains of attosecond pulses. To demonstrate a typical use
of these new XUV light beams, we show our ability to generate and control,
through photoionization, attosecond electron beams carrying OAM. These
breakthroughs pave the route for the study of a series of fundamental phenomena
and the development of new ultrafast diagnosis tools using either photonic or
electronic vortices.
