Theoretical Study of the Accuracy Limits of 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 $1s\mathrm{\text{−}}2s$ resonance and in the one-photon $1s\mathrm{\text{−}}2p$ resonance in a hydrogen atom. This limit for $1s\mathrm{\text{−}}2s$ resonance is found to be $\sim {10}^{-5}\mathrm{Hz}$ compared to the accuracy achieved in experiment $\pm 46\mathrm{Hz}$. In the case of a deuterium atom the limit is essentially larger: ${10}^{-2}\mathrm{Hz}$. For $1s\mathrm{\text{−}}2p$ resonance the accuracy limit is 0.17 MHz while the uncertainty of the recent frequency measurement is about 6 MHz.