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Physical Review A

Differential intracavity phase spectroscopy and its application to a three-level system in samarium

Scott A. Diddams, Jean‐Claude Diels, Briggs W. Atherton

Published Sep 1, 1998• 34 citations
Publisher

Abstract

A technique of differential intracavity phase spectroscopy is introduced. The measured beat frequency between the two counterpropagating fields in a ring laser directly yields the differential phase shift due to the presence of an atomic vapor. In an unstabilized laser cavity, phase differences near ${10}^{\ensuremath{-}6}$ are measured. This technique is used to study the nonlinear dispersion associated with a three-level $\ensuremath{\Lambda}$ system in atomic samarium. Sub-Doppler resonances and population trapping are observed, both of which are attributed to the coherences between the two lower levels of the $\ensuremath{\Lambda}$ level structure. Solutions of the density matrix describing the system are also presented, and good qualitative agreement is found between the calculations and the measurements.

DOI
10.1103/physreva.58.2252

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Annual Meeting Optical Society of America•Jan 1, 1992•0 citations
A technique of differential intracavity phase spectroscopy is introduced. The measured beat frequency between the two counterpropagating fields in a ring laser directly yields the differential phase shift due to the presence of an atomic vapor. In an unstabilized laser cavity, phase differences near 10\ensuremath−6{10}^{\ensuremath{-}6}10\ensuremath−6 are measured. This technique is used to study the nonlinear dispersion associated with a three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system in atomic samarium. Sub-Doppler resonances and population trapping are observed, both of which are attributed to the coherences between the two lower levels of the \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ level structure. Solutions of the density matrix describing the system are also presented, and good qualitative agreement is found between the calculations and the measurements.
Summary form only given. The fact that the two counterpropagating pulses in a modelocked dye ring laser can be completely decoupled in frequency makes such a laser a sensitive probe of phase differences between the counterpropagating pulses. The difference in center frequency between the two counterpropagating pulses can be resolved down to the noise limit of 100 Hz. This limit corresponds to a phase difference between the counterpropagating pulses of 10/sup -6/ or an effective cavity length difference of 10/sup -12/ m. When combined with fluorescence measurements and the intensities of the counterpropagating fields, the steady-state elements of the density matrix describing the intracavity system can be inferred.
Summary form only given. We report on the investigation of the parametric phase shift of a fixed coupling laser field in a lambda type three level system. The parameter under variation is the frequency of the probing field acting on the second transition. In the vicinity of the two photon resonance in this coherent population trapping system the phase of both fixed coupling field and swept probe field undergo a very rapid change. Outside this relatively narrow structure the phase of the probe field follows the usual one photon dispersion line. A semi-classical density matrix model yields analytically expressions for the parametric dispersion and absorption. The system we used was a three level system in the D2 line of cesium obtained from a cesium atomic beam. The phase shift of the coupling beam was measured with a three beam heterodyne interferometer relative to an off-resonant reference laser field. This setup is less sensitive to acoustic and vibrational noise than a homodyne interferometer and provides a reasonable signal to noise ratio even at coupling powers of a few nW. The power of both coupling and probe field was varied over several orders of magnitude and the obtained phase shifts are in good agreement with the semi-classical model.
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.
Resonances of coherent population trapping were detected in atomic vapours of the rare-earth element samarium. The coherent population trapping was produced by two external-cavity diode lasers (672 and 686 nm) in a Λ-system formed by the three levels of 154 Sm: the 4 f 6 6 s 2 ( 7 F 0 ) ground state, the first fine-structure 4 f 6 6 s 2 ( 7 F 1 ) sublevel of the ground state and the 4 f 6 ( 7 F )6 s 6 p ( 3 P o ) 9 F o 1 upper level. The dependence of the spectral shapes and resonance contrasts on the polarisation of the laser beams and the direction of the applied magnetic field was studied. The obtained results were analysed.
In a passively mode-locked femtosecond ring dye laser the two counterpropagating pulses have a relative frequency difference Av that can be adjusted from a few hertz to megahertz by rotation of the cavity. These opposing pairs of pulses can thus be used to establish coherence between sublevels of a A transition in a resonant vapor. Sagnac spectroscopy is the distortion of the (previously linear) Sagnac response of the laser when such an atomic vapor (Sm) is inserted in the cavity. Even though the bandwidth of this unstabilized laser is of the order of 1013 Hz, spectroscopic measurements can be performed with 10 Hz accuracy. Applications include magnetic field measurement, lasing without inversion, and giant index of refraction.