Ultrafast excitation, ionization, and fragmentation of $\mathrm{C_{60}}$

This chapter presents notions, facts, and findings on $C_{60}$ and the fullerenes. The chapter discusses basic terminology and concepts from the area of atoms and molecules in strong fields. Some experimental aspects of studying molecules in intense, short pulse laser fields are addressed. The chapter also explains the ionization process, charge states, and fragmentation after short pulse laser interaction with $C_{60}$ as observed by mass spectroscopy. The intensity dependence of these processes and compares saturation intensities for the ionization processes with simple atomic systems is addressed in the chapter. Further, the above threshold ionization (ATI) observed in photoelectron spectra at various short pulse laser intensities are discussed and compared with the recent theoretical results. Theoretical comparison leads to a critical discussion of the primary excitation mechanism in an intense laser pulse. The chapter also discusses the band structure model in condensed matter, that is, for a semiconductor in the case of $C_{60}$. The chapter illustrates this with an example: the non-resonant excitation of Rydberg states in $C_{60}$. Further, the fast fragmentation processes of $C_{60}$ beyond the established statistical fragmentation processes known to occur on the ns to μs time scale are addressed