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Optics Express

Absorption line broadening in atomic beams produced in a molecular beam epitaxy environment

Roman Rousseau, Jérôme Morville, Claude Botella, Guillaume Saint‐Girons

Published Aug 29, 2024• 1 citation
Publisher

Abstract

absorption line profile of a Ba atomic beam produced in a molecular beam epitaxy (MBE) reactor. Despite the noisy MBE environment, a signal-to-noise ratio up to 100 is obtained thanks to a thorough optimization of the measurement setup. A model that realistically describes this absorption profile is presented, taking into account the angular distribution of atomic concentration in the atomic beam as well as the reactor and setup geometry. Our results highlight the influence of the latter on the Doppler line broadening, and allows to estimate the angular distribution of concentration in the beam emitted by the effusion cell. The model can be adapted to estimate the absorption profile for any element in any reactor geometry, making it a useful tool to design MBE dedicated atomic absorption sensors such as optical flux monitoring sensors, or to characterize the beam emitted by any effusion cell.

DOI
10.1364/oe.536538

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absorption line profile of a Ba atomic beam produced in a molecular beam epitaxy (MBE) reactor. Despite the noisy MBE environment, a signal-to-noise ratio up to 100 is obtained thanks to a thorough optimization of the measurement setup. A model that realistically describes this absorption profile is presented, taking into account the angular distribution of atomic concentration in the atomic beam as well as the reactor and setup geometry. Our results highlight the influence of the latter on the Doppler line broadening, and allows to estimate the angular distribution of concentration in the beam emitted by the effusion cell. The model can be adapted to estimate the absorption profile for any element in any reactor geometry, making it a useful tool to design MBE dedicated atomic absorption sensors such as optical flux monitoring sensors, or to characterize the beam emitted by any effusion cell.
The formation of the Doppler absorption profile P(ν) upon optical excitation of particles in the volume of effusion or gas-dynamic atomic and molecular beams by laser light propagating in a direction orthogonal (reduced) to the beam axis is considered. The analytical expressions for P(ν) are obtained for different types of beams and the specific features of the reduced absorption profile are studied as functions of the beam parameters. The function P(ν) is shown to be considerably different from the standard Gaussian shape. It is demonstrated that the calculated absorption spectrum at the frequencies of the sodium resonance lines D 1,2 agrees well with experiment.
We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2% for the D2 line at 16.5 degrees C.
Abstract. We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2 % for the D2 line at 16.5 ◦ C. PACS numbers: 32.70.-n, 32.70.Fw, 42.62.FiAbsolute Rb absorption 2 1.
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.
Here, we report a measurement scheme for determining an absorption profile with an accuracy imposed solely by photon shot noise. We demonstrate the power of this technique by measuring the absorption of cesium vapor with an uncertainty at the 2-ppm level. This extremely high signal-to-noise ratio allows us to directly observe the homogeneous line-shape component of the spectral profile, even in the presence of Doppler broadening, by measuring the spectral profile at a frequency detuning more than 200 natural linewidths from the line center. We then use this tool to discover an optically induced broadening process that is quite distinct from the well-known power broadening phenomenon.