Theoretical study of the accuracy limits for the optical resonance frequency measurements

The principal limits for the accuracy of the resonance frequency measurements set by the asymmetry of the natural resonance line shape are studied and applied to the recent accurate frequency measurements in the two-photon 1s-2s resonance and in the one-photon 1s-2p resonance in hydrogen atom. This limit for 1s-2s resonance is found to be $\sim 10^{-5}$ Hz compared to the accuracy achieved in experiment $\pm 46$ Hz. In case of deuterium atom the limit is essentially larger: $10^{-2}$ Hz. For 1s-2p resonance the accuracy limit is 0.17 MHz while the uncertainty of the recent frequency measurement is about 6 MHz.Comment: to be published in Physical Review Letter