Stable diode lasers for hydrogen precision spectroscopy

We report on an external cavity diode laser at 972 nm stabilized to a mid-plane mounted Fabry-Perot (FP) resonator with a finesse of 400000. The 0.5 Hz optical beat note line width between two similar lasers (Allan deviation 2 x 10(-15)) is limited by thermal noise properties of two independent FP resonators. The long term drift of the FP resonator and mirror substrates made from Ultra-Low-Expansion glass (ULE) is small and can be well predicted on time intervals up to many hours if the resonator is stabilized at the zero thermal expansion temperature T-c. Using a Peltier element in a vacuum chamber for temperature stabilization allows stabilization of the FP cavity to T-c which is usually below the room temperature. Beat note measurements with a femtosecond optical frequency comb referenced to a H-maser during 15 hours have shown a well defined linear drift of the FP resonance frequency of about 60 mHz/s with residual frequency excursions of less than +/- 20 Hz.