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Physical Review A

Coherence phenomena in phase-modulation laser spectroscopy

Ralph G. DeVoe, Richard G. Brewer

Published Jul 1, 1982• 10 citations
Publisher

Abstract

The technique of phase-modulation laser spectroscopy is used to detect a coherent four-wave interaction in ${\mathrm{I}}_{2}$ vapor. A phase-modulated probe beam induces in the sample an oscillating population which in turn modulates a counterpropagating pump beam that reveals a characteristic two-resonance spectrum. The observations fully confirm an earlier density-matrix calculation.

DOI
10.1103/physreva.26.705

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The technique of phase-modulation laser spectroscopy is used to detect a coherent four-wave interaction in I2{\mathrm{I}}_{2}I2​ vapor. A phase-modulated probe beam induces in the sample an oscillating population which in turn modulates a counterpropagating pump beam that reveals a characteristic two-resonance spectrum. The observations fully confirm an earlier density-matrix calculation.
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.
A new source of two diode laser beams, spatially separated but optically phase-locked with each other, is used to study the modulation transfer spectroscopy of coherent population trapping resonance (CPT). The spectrum for the (87)Rb D2 line is obtained with narrow linewidth and high signal-to-noise ratio, and analyzed with different experimental parameters. A theoretical analysis of the CPT modulation transfer spectra is deduced from the density matrix equation of motion, and found to be in good agreement with the experimental results.
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Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations