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Optics Letters

Doppler-free two-photon heterodyne spectroscopy by single-beam frequency modulation

M. Ducloy

Published Sep 1, 1982• 10 citations
Publisher

Abstract

A new spectroscopic method for monitoring Doppler-free two-photon absorption signals is analyzed. Its principle consists of high-frequency modulation of one of the incident beams and the detection of the modulation induced by two-photon absorption in the intensity of the counterpropagating beam. The predictable advantages of this method are pointed out by comparing it with other techniques.

DOI
10.1364/ol.7.000432

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Physical Review A•May 1, 1982•88 citations
A new spectroscopic method for monitoring Doppler-free two-photon absorption signals is analyzed. Its principle consists of high-frequency modulation of one of the incident beams and the detection of the modulation induced by two-photon absorption in the intensity of the counterpropagating beam. The predictable advantages of this method are pointed out by comparing it with other techniques.
Heterodyne Doppler-free spectroscopy, previously demonstrated on single-photon resonances (heterodyne saturation spectroscopy), has been extended to two-photon transitions in rubidium (5S-5D and 5S-7S). It provides a simple method of observing the two-photon dispersion lineshape directly. The noticeable sensitivity of this absorption technique, which has been used for an optical measurement of the hyperfine structure of the 5D level, is discussed in comparison with that currently obtained in two-photon-induced fluorescence.
In this article, we analyse a new sensitive spectroscopic technique in which a sample cell is irradiated by a two-frequency pump beam (ω + Δ ± δ/2) and a counter-propagating probe beam (ω). The phase-conjugate fields re-emitted at frequencies ω ± δ, via four-wave mixing processes, are detected through their heterodyne beating with the probe field. The properties of the heterodyne beat signal are studied by means of a perturbation calculation of the nonlinear response of the medium, carried out to the third order in the incident fields. In resonant gas media, the emission lineshape exhibits a Doppler-free doublet structure [frequency splitting 3 δ/2 for single-photon resonances, and δ/2 for two-photon transitions]. By using a phase-sensitive detection of the beat signal, one can separately analyse real (dispersion) or imaginary parts (absorption) of the nonlinear susceptibility. For single-photon transitions, the signal phase shift is related to the atomic levels lifetime and allows one to study the relaxation dynamics in gas phase (like quenching collisions, velocity diffusion, etc...). This is particularly interesting for cross-over resonances, in which only the common level contributes. In three-level systems, one also predicts a selective resonant enhancement of the phase-conjugate emission through Raman-type two-photon processes. Most of these predictions have been experimentally verified.
Optical heterodyne spectroscopy is one of the ultrasensitive and high resolution laser spectroscopies. During past years, it has extended from saturation absorption to two-photon transitions in a three level quantum system of atoms and ions. The particularly interesting case is the modulation transfer spectroscopy, where the optical heterodyne detection is performed via nearly degenerate four-wave mixing (NDFWM) in the nonlinear medium. In this report, the modulation transfer spectroscopy is used to observe the optical heterodyne saturation absorption and two-photon transition spectra simultaneously in Na2 without Doppler background. The line shapes of optical heterodyne signal are discussed in detail.
Combined with the modulation transfer method, we successfully observe a frequency discriminating signal with improved signal-to-noise ratio (SNR) in the scheme of differential detection of Doppler-free spectroscopy. In our previous counter-propagated pump-probe scheme, two orthogonal polarization components of the probe beam constrictive and destructive interact with dark state prepared by the pump beam, respectively. This led to simultaneous enhanced absorption and transmission by detecting the parallel and perpendicular polarization components of the transmitted probe beam. In this presentation, we add modulation to the pump beam, error signals are obtained by synchronous demodulating the probe beam transmission with the help of the four-wave mixing process in the light-atom interaction system. Our method not only boost the SNR of the error signal of differential detection signal compared to the traditional one, but also mitigate atomic resonance broadening and shift induced by direct modulation of the probe beam thanks to the modulation transfer spectroscopy. This new method may find applications in high-performance optical reference, high-resolution spectroscopy and so on.
A novel phase-modulation technique which permits subkilohertz-laser stability and new levels of precision in laser spectroscopy was reported recently. For spectroscopy, the basic arrangement consists of a combination of an optical pump and a probe field which is phase modulated. The pump prepares the atomic sample by burning a narrow hole within the atom's inhomogeneous line shape, and the probe beam samples the prepared hole when its modulation sidebands are swept into resonance. Off resonance, the probe is balanced as pairs of sidebands produce heterodyne beat signals of opposite phase which just cancel. On resonance, the balance is upset and yields a nonvanishing beat signal with a Lorentzian absorption or dispersion line shape and with residual noise approaching the shot noise limit. Here we investigate the theory of phase-modulation spectroscopy. We treat the nonlinear response of an atomic two-level quantum system subject to an intense pump and a weak copropagating or counterpropagating phase-modulated probe beam. The density-matrix equations of motion are solved by a Laplace-transform method and by the novel use of a translation operator which allows the infinite hierarchy of coupled equations to close. A solution equivalent to the rate-equation result is developed and coherence corrections are found which predict new resonances that have just been detected in this laboratory. The delayed pump-probe technique encountered in solid-state laser spectroscopy is analyzed in this context for two- and three-level quantum systems. The response of a Fabry-Perot cavity to a phase-modulated light wave is examined also and reveals an unexpected absorption feature.