Stabilization of mode-locked trains, and dark resonance of two-photon lambda-level structures

Our ultimate objective is to design a combined frequency standard for optical as well as radio frequencies. A mode-locked laser provides frequency components that can be used as a ruler to measure any unknown optical source through direct beating. The frequency spacing of a pair of teeth of this comb is in itself a radio frequency reference. Fast control and correction for both the average frequency and the repetition rate of a mode-locked Ti:sapphire laser are achieved by locking the laser to a reference cavity of ultra-low expansion quartz with equal mode spacing. We measure an optical frequency with a mean square deviation of 700 Hz, instability limited by the radio-frequency sources used to count the repetition rate. As a reference standard to achieve absolute accuracy, we use the Λ transition 5S^1/2(F = 1) → 5D^5/2(F = 3) → 5S^1/2(F = 2) of rubidium. The theory for this coherent interaction shows that, with one mode resonant with the two-photon 5S^1/2(F = 1) → 5D^5/2(F = 3) transition, the fluorescence goes through a resonance for a change in repetition rate of less than 10kHz. These results suggest that, by locking to the peak of that resonant feature, optical stability and absolute accuracy better than 1 kHz can easily be achieved.