in the frequency calibration. For further details on the two-photon Doppler-free laser experiments on CO we refer to previous publications [@Niu2013; @Niu2015].

![ The S(0) transition in the [A$^1\Pi-$X$^1\Sigma^+$]{}$(0,0)$ band of $^{13}$C$^{16}$O, as measured via two-photon Doppler-free laser spectroscopy, plotted as a black line. The red and blue lines show the saturated iodine spectrum and etalon markers used for calibration and interpolation. The asterisk (\*) indicates the hyperfine component of the iodine line used for the absolute wave number calibration, in this case with overlapping contributions from the $a_5$ and $a_6$ components of the B$-$X$(8,2)$ $R(81)$ line at $16\,190.06605$ and $16\,190.06616$ [cm$^{-1}$]{} [@Bodermann2002; @Xu2000]. The upper scale represents the fundamental wave number of the cw-seed laser, and the lower scale the two-photon excitation energy.[]{data-label="fig:PDAspec"}](PDAspectrum3.eps){width="\linewidth"}

![Wave number of the S(0) transition of the [A$^1\Pi-$X$^1\Sigma^+$]{}$(0,0)$ band of $^{13}$C$^{16}$O extrapolated to zero probe-laser power, yielding an AC-Stark shift corrected value.[]{data-label="fig:stark"}](starkplot.eps){width="\linewidth"}

The sources of transition-frequency uncertainty in the laser experiment were investigated. The statistical uncertainty was estimated from multiple measurements of the observed lines to be 30 MHz. The frequency chirp of the fundamental radiation was measured to be $-11\pm 2$MHz, leading to a $-44$MHz correction to the measured [A$^1\Pi-$X$^1\Sigma^+$]{} frequencies with a residual 