  The electro-optical properties of most semiconductors and insulators of
technological interest are dominated by the presence of electron-hole
quasiparticles called excitons. The manipulation of these hydrogen-like
quasi-particles in dielectrics, has received great interest under the name
excitonics that is expected to be of great potential for a variety of
applications, including optoelectronics and photonics. A crucial step for such
exploitation of excitons in advanced technological applications is a detailed
understanding of their dynamical nature. However, the ultrafast processes
unfolding on few-femtosecond and attosecond time scales, of primary relevance
in view of the desired extension of electronic devices towards the petahertz
regime, remain largely unexplored. Here we apply attosecond transient
reflection spectroscopy in a sequential two-foci geometry and observe
sub-femtosecond dynamics of a core-level exciton in bulk MgF$_2$ single
crystals. With our unique setup, we can access absolute phase delays which
allow for an unambiguous comparison with theoretical calculations based on the
Wannier-Mott model. Our results show that excitons surprisingly exhibit a dual
atomic- and solid-like character which manifests itself on different time
scales. While the former is responsible for a femtosecond optical Stark effect,
the latter dominates the attosecond excitonic response and originates by the
interaction with the crystal. Further investigation of the role of exciton
localization proves that the bulk character persists also for strongly
localised quasi-particles and allows us to envision a new route to control
exciton dynamics in the close-to-petahertz regime.
