Spectral narrowing of atomic resonance by recurrent excitation spectroscopy: Feedback from atom to radiation field via digital-data processing

We describe the theoretical analysis and experimental detail of recurrent excitation spectroscopy (RES), which contributes to precise determination of atomic resonance frequency. The basic idea of RES lies in the iterative excitation of the atomic system by radiation. During the preceding excitation, the output held emitted from the atom is recorded in the form of digital data, and the next excitation field is generated in accordance with these data. This recurrent interaction between the atomic system and the radiation field significantly reduces the spectral width of the atomic resonance, while the signal-to-noise ratio remains sufficiently high. To reflect the actual experimental situation, we present a theoretical model in the presence of background white noise, and using this model, analytical and numerical calculations are performed. We find that RES gives a better signal-to-noise ratio compared to the conventional averaging technique until spectral narrowing is terminated. The combination of RES and the digital-data processing technique has been successfully applied to the magnetic resonance of Rb atoms in the sub-MHz region, where our theoretical findings are experimentally confirmed.