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Journal de physique

Doppler-free two-photon spectroscopy of neon. II. Line intensities

G. Grynberg, F. Biraben, E. Giacobino, Bernard Cagnac

Published Jan 1, 1977• 56 citations
Publisher

Abstract

We report in this paper the principle of the calculation of the hyperfine components of a two-photon absorption line and we compare the results of the calculation with some of our expérimental results. In the first part of the paper, the two-photon transition operator is expanded on a tensorial irreductible set basis. That operator is generally the sum of two operators, one scalar and the other one quadrupolar. We deduce from it the selection rules for two-photon absorption and the formulae which permit one to calculate the intensities of the hyperfine components of a two-photon absorption line. We also report the density matrix in the excited state obtained after the two-photon excitation process, which permits one to calculate the fluorescence lines. At last we present the atomic quantities involved in the collision broadening of a two-photon absorption line. In the second part, we present the experimental hyperfine spectra obtained on the neon 21 atom for the transitions between the 3s[3/2] 2 metastable level and the 4d'[5/2] 2, 4d'[3/2] 2 and 4d[3/2] 2 excited levels. We show that the expérimental ratios between the scalar and the quadrupolar parts are very different from one transition to another. At last we compare these ratios with theoretical values obtained using the formulae of the first part. We find a good agreement between expérimental and theoretical values.

DOI
10.1051/jphys:01977003806062900

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We report in this paper the principle of the calculation of the hyperfine components of a two-photon absorption line and we compare the results of the calculation with some of our expérimental results. In the first part of the paper, the two-photon transition operator is expanded on a tensorial irreductible set basis. That operator is generally the sum of two operators, one scalar and the other one quadrupolar. We deduce from it the selection rules for two-photon absorption and the formulae which permit one to calculate the intensities of the hyperfine components of a two-photon absorption line. We also report the density matrix in the excited state obtained after the two-photon excitation process, which permits one to calculate the fluorescence lines. At last we present the atomic quantities involved in the collision broadening of a two-photon absorption line. In the second part, we present the experimental hyperfine spectra obtained on the neon 21 atom for the transitions between the 3s[3/2] 2 metastable level and the 4d'[5/2] 2, 4d'[3/2] 2 and 4d[3/2] 2 excited levels. We show that the expérimental ratios between the scalar and the quadrupolar parts are very different from one transition to another. At last we compare these ratios with theoretical values obtained using the formulae of the first part. We find a good agreement between expérimental and theoretical values.
A theory of the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.
In this paper, we describe two complementary nonlinear spectroscopy methods which both allow one to achieve Doppler-free spectra of atomic gases. First, saturated absorption spectroscopy is used to investigate the structure of the 5S 1/2 → 5P 3/2 transition in rubidium. Using a slightly modified experimental setup, Doppler-free two-photon absorption spectroscopy is then performed on the 5S 1/2 → 5D 5/2 transition in rubidium, leading to accurate measurements of the hyperfine structure of the 5D 5/2 energy level. In addition, electric dipole selection rules of the two-photon transition are investigated, first by modifying the polarization of the excitation laser, and then by measuring two-photon absorption spectra when a magnetic field is applied close to the rubidium vapour. All experiments are performed with the same grating-feedback laser diode, providing an opportunity to compare different high-resolution spectroscopy methods using a single experimental setup. Such experiments may acquaint students with quantum mechanics selection rules, atomic spectra and Zeeman effect.
Abstract We theoretically and experimentally investigate the Doppler-broadened absorption spectrum of the D2-line (52 S 1/2 → 52 P 3/2) in thermal (room-temperature) Rb vapour over a wide range of probe intensity, probe diameter, and vapour cell temperature to understand the effect of hyperfine pumping and transit-relaxation on the absorption lineshape. We present a relatively simple but comprehensive five-level rate equation model which incorporates optical pumping of the atomic population into the other ‘dark’ ground hyperfine level (leading to absorption saturation), including contributions of the three closely spaced (within one Doppler linewidth) hyperfine levels in the excited state 52 P 3/2 (allowed by the dipole transition selection rules). D2-line transmission spectra predicted by our model show excellent agreement (rms error < 5 % ) with the experimental data for a wide range of probe intensities (from ∼ 0.001 I s a t 0 all the way up to ∼ 10 I s a t 0 , where I sat0 is the usual two-level saturation intensity for the respective atomic transition), vapour cell temperatures (24.2°C–53.5 °C) and beam diameters (1/e 2 width ∼ 1 − 6 mm). Our model also takes into account the finite transit time of atoms across the probe beam cross-section, and correctly predicts the dependence of effective saturation intensity on probe diameter (up to ∼ 10 × lower saturation intensity as compared to I sat0 for few-mm beam sizes). This ab initio five-level model can thus predict accurate Doppler lineshapes for any given experimental parameter set for a linearly polarized probe without any fitting parameters, and can be easily applied to any other atomic system by an appropriate change of the atomic constants in the rate equations.
The probability of a two-photon absorption (TPA) process is quantified by means of the TPA cross-section. In this work the TPA cross-section for the 6 S 1/2 → 8 S 1/2 transition in cesium (Cs) atoms is obtained from a theoretical and experimental approach. It is calculated using second order perturbation theory including hyperfine structure and Doppler broadening for a thermal atomic vapor. The theoretical values for the TPA cross-sections of the two allowed hyperfine transitions are σ ~ 3,3 =3.10×10 −24 cm 4 /W and σ ~ 4,4 =3.65×10 −24 cm 4 /W. An experiment is set up to measure these cross-sections based on the quadratic dependence between the TPA transition rate and the intensity of the laser light. Values of σ ~ 3,3 =(3.6±1.1)×10 −24 cm 4 /W and σ ~ 4,4 =(4.6±1.1)×10 −24 cm 4 /W are obtained from the measurements. The results show an agreement between theory and experiment. To the best of our knowledge, this is the first time that these cross-sections are reported.