Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Femtosecond frequency combs emitted from mode-locked lasers have recently enabled a new generation of ultra-precise optical clocks, whose stability can greatly surpass that of the best atomic clocks. This progress has potential applications to fundamental physics and technology (e.g., spectroscopy, navigation, etc). We show a remarkable agreement between the theory of dispersion and nonlinearity-managed solitons and experiments with mode-locked Ti:sapphire lasers. In addition, optical clocks require control over the carrier-envelope phase slip in the laser cavity. A simple asymptotic formula is derived for the deterministic nonlinear phase slip. Finally, Spontaneous Emission (quantum) noise broadens the comb lines. Asymptotic scaling laws are found for the random linewidth of the comb lines, which shows some of the important differences between the linear and nonlinear regimes.