Precision spectroscopy of the simple hydrogen atom has inspired dramatic advances in optical frequency metrology: femtosecond laser optical frequency comb synthesizers have revolutionized the precise measurement of optical frequencies, and they provide a reliable clock mechanism for optical atomic clocks. Precision spectroscopy of the hydrogen 1S–2S two-photon resonance has reached an accuracy of 1.4 parts in 10
14
, and considerable future improvements are envisioned. Such laboratory experiments are setting new limits for possible slow variations of the fine structure constant
α
and the magnetic moment of the caesium nucleus
μ
Cs
in units of the Bohr magneton
μ
B
.
Stabilization of femtosecond laser frequency combs with subhertz residual linewidths