We present full phase stabilization of an amplified Yb:fiber femtosecond frequency comb using an intra-cavity electro-optic modulator and an acousto-optic modulator. These transducers provide high servo bandwidths of 580 kHz and 250 kHz for frep and
fceo, producing a robust and low phase noise fiber frequency comb. The comb was self-referenced with an f - 2f interferometer and phase locked to an ultra-stable optical reference used for the JILA Sr optical clock at 698 nm, exhibiting 0.21 rad and 0.47 rad of integrated phase errors (over 1 mHz - 1 MHz) respectively. Alternatively, the comb was locked to two optical references at 698 nm and 1064 nm, obtaining 0.43 rad and 0.14 rad of integrated phase errors respectively.
We explore the potential of direct spectroscopy of ultra-narrow optical transitions of atoms localized in an optical cavity. In contrast to stabilization against a reference cavity, which is the approach currently used for the most highly stabilized
lasers, stabilization against an atomic transition does not suffer from Brownian thermal noise. Spectroscopy of ultra-narrow optical transitions in a cavity operates in a very highly saturated regime in which non-linear effects such as bistability play an important role. From the universal behavior of the Jaynes-Cummings model with dissipation, we derive the fundamental limits for laser stabilization using direct spectroscopy of ultra-narrow atomic lines. We find that with current lattice clock experiments, laser linewidths of about 1 mHz can be achieved in principle, and the ultimate limitations of this technique are at the 1 $mu$ Hz level.
