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Japanese Journal of Applied Physics

Spectral Narrowing of Atomic Resonance by Recurrent Excitation Spectroscopy: Feedback from Atom to Radiation Field via Digital-Data Processing

Takahisa Mitsui, Tohru Kinugawa, Katsumi Sakurai

Published Feb 1, 1999• 7 citations
Publisher

Abstract

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 field 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.

DOI
10.1143/jjap.38.923

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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 field 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.
Summary form only given. To understand the fundamental properties of an atom, precise measurement of the atomic resonance frequency is important. The main factor that restricts the precision is the spectral broadening. Spectral narrowing by recurrent use of free decay signal in magnetic resonance was proposed and demonstrated in the ground state of Rb atoms. In the present report we apply this technique to the measurement of the hyperfine frequency in the excited state. This is a sublevel spectroscopy with recurrent excitation, where the atomic response is iteratively used as the next excitation. The hyperfine spectra of the excited state /sup 2/P/sub 3/2/ of the D/sub 2/ transition in Rb atoms, whose line width is much narrower than the natural line width, was observed and the hyperfine constants of the excited state were determined precisely.
Summary form only given. Spectral narrowing by recurrent use of free-decay signal in magnetic resonance has been proposed and demonstrated in the ground state of Rb atoms. In the present report we apply this technique to the measurement of the hyperfine frequency in the excited state. This is a sublevel spectroscopy with recurrent excitation where the atomic response is iteratively used as the next excitation. The hyperfine spectra of the excited state /sup 2/P/sub 3/2/ of the D/sub 2/ transition in /sup 85/Rb atoms, the line widths of which are much narrower than the natural width, were observed and the hyperfine constants of the excited state were determined precisely.
We propose a new type of spectroscopic method to reduce spectral width by recurrently using free decay (FD) in magnetic resonance of transverse optical pumping. Simultaneously with the excitation of the atomic system by a pump beam, the induced FD signal was recorded by a digital waveform memory. Then, in order to induce the next FD, we excited the atomic system by a pump beam, the intensity of which was modulated by the recorded FD, and recorded the FD induced by this pump beam. Recurrent use of this procedure reduced the spectral width of the atomic resonance and increased the signal-to-noise ratio. The narrowing procedure was demonstrated by using a randomly modulated stationary pump beam. Theoretical and experimental studies are presented. Our method serves to increase the precision of the measurement of the centre frequency of the atomic resonance.
A critical examination of the theory of resonance radiation has been carried through, employing the mathematical technique of Laplace and Stieltjes transforms. Particular attention has been devoted to the question of the temporal behavior of the excited state. With no restrictions on the interaction between atom and radiation field other than that it be real, and that processes of sufficiently high frequency contribute only negligible effects, one can prove that the probability amplitude of the excited state cannot decay according to the general law ${\ensuremath{\Sigma}}_{\ensuremath{\mu},\ensuremath{\nu}}{C}_{\ensuremath{\mu}\ensuremath{\nu}}{t}^{{\ensuremath{\lambda}}_{\ensuremath{\mu}}}{e}^{\ensuremath{-}{\ensuremath{\beta}}_{\ensuremath{\nu}}t},$ where the ${\ensuremath{\lambda}}_{\ensuremath{\mu}}$ and ${\ensuremath{\beta}}_{\ensuremath{\nu}}$ are complex constants lying in the right half-plane and the ${C}_{\ensuremath{\mu}\ensuremath{\nu}}$ are arbitrary complex coefficients. The deviation from the law just cited can be termed a straggling phenomenon since exact analysis shows that the probability amplitude, for sufficiently long times, is greater than that defined according to the radioactive decay law.Rigorous analysis of the source of this apparently anomalous behavior reveals the following explanation. Although the probability amplitude of the excited state is, strictly speaking, a functional of the interaction between the transition current in the atom and the photon states of the electromagnetic field, the essential features are determined principally by those states lying near the resonance frequency. Three elementary observations are immediately apparent. First, a particularly tractable analytical approximation for the interaction can be made such that the value of the actual interaction is reproduced at the resonance frequency and such that the behavior for high and low frequency photon states is at least qualitatively correct. Exact solutions in closed form can be obtained for this interaction. Second, in terms of the preceding representation it is possible to show that, associated with the transition between two atomic states, one is presented with a concomitant picture of a damped oscillation of charge describable in purely classical terms. Third, this classical motion can be interpreted as forming a source function for a continuous stochastic process in terms of which one finally derives the representation of the probability amplitude of the excited state. The straggling phenomenon previously cited is therefore that associated with all diffusion processes. The consideration of the exact interaction leads to more involved diffusion phenomena but does not in any case permit a radioactive decay law.
The spectra of three-photon laser excitation (according to the 5 S 1/2 → 5 P 3/2 → 6 S 1/2 → 37 P 3/2 scheme) of mesoscopic ensembles of cold Rb Rydberg atoms in a magneto-optical trap, using cw single-frequency lasers in each stage, have been investigated. The ensembles consisted of 1 to 5 atoms, and their presence was recorded by the selective field ionisation method with postselection according to the number of atoms. The dependence of the spectral shape on the excitation laser pulse duration has been studied. For 2-μs pulses, the minimum spectral width was found to be 1.3 MHz; it was determined by the laser linewidth and the spectral width of laser pulse. For pulses shorter than 0.5 μs, additional spectral broadening and occurrence of Rabi oscillations in the wings of three-photon resonances have been observed, a fact indicative of implementation of coherent three-photon laser excitation of Rydberg atoms. An analysis of the spectra within the four-level theoretical model based on optical Bloch equations showed good agreement between the experimental and theoretical results. The dependence of the shape of three-photon excitation spectrum on the number of recorded atoms was also studied. An increase in the average number of atoms leads to the occurrence of a dip in the single-atom excitation spectra; this dip is due to the specificity of the excitation and detection statistics of Rydberg atoms. The results obtained are important for applications of Rydberg atoms in quantum informatics.