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.
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