Optical frequency stabilization of a 10 GHz Ti:sapphire frequency comb by saturated absorption spectroscopy in ⁸⁷rubidium

The high power per mode of a recently developed 10 GHz femtosecond Ti:sapphire frequency comb permits nonlinear Doppler-free saturation spectroscopy in ⁸⁷Rb with a single mode of the comb. We use this access to the natural linewidth of the rubidium D₂ line to effectively stabilize the optical frequencies of the comb with an instability of 7×10⁻¹² in 1 s of averaging. The repetition rate is stabilized to a microwave reference leading to a stabilized and atomically referenced comb. The frequency stability of the 10 GHz comb is characterized using optical heterodyne with an independent self-referenced 1 GHz comb. In addition, we present alternative stabilization approaches for high repetition rate frequency combs and evaluate their expected stabilities.