  Silicon-vacancy color centers in nanodiamonds are promising as fluorescent
labels for biological applications, with a narrow, non-bleaching emission line
at 738\,nm. Two-photon excitation of this fluorescence offers the possibility
of low-background detection at significant tissue depth with high
three-dimensional spatial resolution. We have measured the two-photon
fluorescence cross section of a negatively-charged silicon vacancy (SiV$^-$) in
ion-implanted bulk diamond to be $0.74(19) \times 10^{-50}{\rm cm^4\;s/photon}$
at an excitation wavelength of 1040\,nm. In comparison to the diamond nitrogen
vacancy (NV) center, the expected detection threshold of a two-photon excited
SiV center is more than an order of magnitude lower, largely due to its much
narrower linewidth. We also present measurements of two- and three-photon
excitation spectra, finding an increase in the two-photon cross section with
decreasing wavelength, and discuss the physical interpretation of the spectra
in the context of existing models of the SiV energy-level structure.
