Line shapes in modulation resonance

Svenja A. Knappe, M. St�hler, C. Affolderbach +3 more

A. Nagel

The line shapes of coherent population trapping resonances have been measured with high resolution and signal-to-noise ratio using a frequency-modulation technique with subsequent deconvolution of the line shapes. Simple models allow a perfect modeling of the experimental line shapes.

Peter Jungner, Birger Stahlberg, Tomas Fellman +1 more

John G. Coffer, Brett A. Sickmiller, A. Presser +1 more

When atoms interact with a phase-modulated field, the probability of finding the atom in the excited-state oscillates at the second harmonic of the modulation frequency, $2{\ensuremath{\omega}}_{m}.$ The amplitude of this oscillating probability is a resonant function of the Rabi frequency \ensuremath{\Omega}, and this is termed a \ensuremath{\beta} Rabi resonance. In this work, we examine the line shape of the \ensuremath{\beta} Rabi resonance both theoretically and experimentally. We find that a small-signal theory of the \ensuremath{\beta}-Rabi-resonance condition captures much of the line shape's character, and, in particular, that the resonance's ``line Q'' (i.e., $2\ensuremath{\delta}{\ensuremath{\Omega}}_{1/2}/\ensuremath{\Omega})$ is proportional to the modulation frequency. This result can be applied to the atomic candle, where \ensuremath{\beta} Rabi resonances are employed to stabilize field strength. Considering our results in the context of developing an optical atomic candle, we find that a free-running diode laser's intensity noise could be improved by orders of magnitude using the atomic candle concept.

Lewis S. Klein

Minora Hashimoto, Motoichi Ohtsu

Novel spectral line shapes of optical-microwave double resonance with an extremely narrow line width were observed in a rubidium atomic clock pumped by a semiconductor laser. It was confirmed that these novel spectral line shapes of double resonance were due to the modulation-transfer effect. These spectral line shapes were calculated by solving the equation of motion of the density matrix that describes the modulation-transfer process. The calculated results agree with the experimental results. By using the calculated results of the influence of the optical Stark effect on these spectral line shapes, characteristics of the inhomogeneous light shift were evaluated quantitatively for the frequency-modulated microwave. Furthermore, optimum values of modulation parameters were found by computer simulation in order to obtain the highest microwave frequency stability of the atomic clocks. An experiment was carried out employing these optimum parameters, and a short-term frequency stability as high as σy(τ) = 7.9 × 10−13τ−1/2 was obtained, where τ is an integration time of measurement.