  We have demonstrated simultaneous laser frequency stabilization of a UV and
IR laser, to the same spectroscopic sample, by monitoring only the absorption
of the UV laser. For trapping and cooling Yb$^{+}$ ions, a frequency stabilized
laser is required at 369.95nm to drive the $^{2}S_{1/2}$ $ \rightarrow $ $
^{2}P_{1/2}$ cooling transition. Since the cycle is not closed, a 935.18nm
laser is needed to drive the $^{2}D_{3/2}$ $\rightarrow$ $^{3}D_{[3/2]1/2}$
transition which is followed by rapid decay to the $^{2}S_{1/2}$ state. Our
369nm laser is locked to Yb$^{+}$ ions generated in a hollow cathode discharge
lamp using saturated absorption spectroscopy. Without pumping, the metastable
$^{2}D_{3/2}$ level is only sparsely populated and direct absorption of 935nm
light is difficult to detect. A resonant 369nm laser is able to significantly
populate the $^{2}D_{3/2}$ state due to the coupling between the levels. Fast
re-pumping to the $^{2}S_{1/2}$ state, by 935nm light, can be detected by
observing the change in absorption of the 369nm laser using lock-in detection
of the photodiode signal. In this way simultaneous locking of two optical
frequencies in very different spectral regimes is accomplished. A rate equation
model gives good qualitative agreement with the experimental results. This
technique offers improved laser frequency stabilization compared to lasers
locked individually to the sample and should be readily applicable to similar
ion systems.
