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Journal of Physics B Atomic Molecular and Optical Physics

Combined effect of non-linear optical and collisional processes on absorption saturation in a dense rubidium vapour

A. J. van Lange, P. van der Straten, D. van Oosten

Published Mar 13, 2020• 10 citations
Publisher

Abstract

Abstract We study non-linear absorption of intense monochromatic light through a dense natural rubidium (Rb) vapour. We measure transmission through a 10 cm long heated vapour cell for atom densities up to 3 × 1019 m−3 and saturation parameters up to 104, for linear and circular polarisation, close to resonance on the 87Rb D2 F = 1 → F′ = 0, 1, 2 transition. The strong absorption at low intensity is frustrated by an interplay of optical non-linearities (saturation and optical pumping) and non-linear effects due to the high atom density (collisional broadening and collisional depumping). To understand the results of the transmission measurements, we developed a model that incorporates these non-linear effects into the optical absorption. The model takes into account the absolute line strengths of all transitions from both hyperfine levels of the ground state of both isotopes of naturally abundant Rb. Doppler and collisional broadening are included in the Voigt profiles for the resonances. We show the effect of each of the non-linear processes on the calculation results of the model, and from comparison with experiment we conclude that all non-linear effects are necessary for a quantitative agreement.

DOI
10.1088/1361-6455/ab7fc2

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New Journal of Physics•Feb 18, 2025•4 citations
Abstract We study non-linear absorption of intense monochromatic light through a dense natural rubidium (Rb) vapour. We measure transmission through a 10 cm long heated vapour cell for atom densities up to 3 × 1019 m−3 and saturation parameters up to 104, for linear and circular polarisation, close to resonance on the 87Rb D2 F = 1 → F′ = 0, 1, 2 transition. The strong absorption at low intensity is frustrated by an interplay of optical non-linearities (saturation and optical pumping) and non-linear effects due to the high atom density (collisional broadening and collisional depumping). To understand the results of the transmission measurements, we developed a model that incorporates these non-linear effects into the optical absorption. The model takes into account the absolute line strengths of all transitions from both hyperfine levels of the ground state of both isotopes of naturally abundant Rb. Doppler and collisional broadening are included in the Voigt profiles for the resonances. We show the effect of each of the non-linear processes on the calculation results of the model, and from comparison with experiment we conclude that all non-linear effects are necessary for a quantitative agreement.
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.
The commonly quoted saturation intensity of rubidium (Rb) for D2 transitions is 16.7W.m−2\mathrm{W}.\mathrm{m}^{-2}W.m−2. This value, however, is only accurate for the cycling transition, which renders the Rb atom to resemble a two-level system. In practice, the effective saturation intensity is influenced by various factors, such as the polarization of light, optical pumping, and atom collision which can redistribute the population. As a result, it is crucial to experimentally determine the effective saturation intensity. In this context, we demonstrate a novel yet simple experimental method to measure the effective saturation intensities of Doppler-broadened transitions in atomic vapours. Our method only requires on-resonance absorbance data for various input laser intensities, which can be obtained with a tunable CW laser without the need for precise frequency locking. We applied this method to measure the effective saturation intensities of all four Doppler-broadened D2 transitions in natural rubidium (Rb) vapour (27.8%87Rb and 72.2 %85Rb{}^{\text{8}} {}^{\text{5}}Rb85Rb) atr=35∘Cr={35}^{\circ} \mathrm{C}r=35∘C. The results show that the effective saturation intensities for Rb range from 0.752 to 16.8W.m−2\mathrm{W}.\mathrm{m}^{-2}W.m−2. Notably, for certain transitions (specifically, repump transitions), the effective saturation intensities were smaller than 16.7 W.m−2\mathrm{m}^{-2}m−2(up to an order of magnitude), with potentially important implications for optical pumping in Doppler-broadened transitions.
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.
This thesis presents a comparative study of the measured and calculated absolute absorption and dispersion properties of the Rb D lines through a dense thermal vapour in the absence and presence of an applied magnetic field. A detailed theoretical model valid in the weak-probe regime is calculated. The model uses a matrix representation of the atomic Hamiltonian including the magnetic field interaction for Rb in the completely uncoupled basis. Numerical diagonalisation allows the frequency detunings and transition strengths to be calculated. The lineshape of each transition is modelled as a Voigt profile, a convolution of the inhomogeneous and homogeneous profiles. The medium’s susceptibility is found by summing over all the electric-dipole-allowed transitions. For dense thermal vapours a modification to the homogeneous linewidth of each transition, which grows linearly with the number density of atoms, arises due to resonant dipole-dipole interactions between identical atoms in superpositions of the ground and excited terms. In the presence of an applied magnetic field we investigate the Stokes parameters of light propagating through a dense thermal vapour. For fields larger than 0.33 T we enter the hyperfine Paschen-Back regime on the Rb D lines. We present a compact optical isolator based on an atomic vapour, exploiting the spectral region of high transmission and large dispersion where we would normally expect absorption on the Rb D lines. Frequency up-conversion is shown in the fluorescence measurements over the visible and near infra-red regions for strong excitation. Low density transfer arises due to the energy-pooling effect between two identical atoms in their first excited terms. At high densities resonant dipole-dipole interactions give rise to a threshold for the energy transfer. We characterise the threshold behaviour with increasing number density.
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 Laser spectroscopy of hot atomic vapours has been studied extensively. Theoretical models that predict the absolute value of the electric susceptibility are crucial for optimising the design of photonic devices that use hot vapours, and for extracting parameters, such as external fields, when these devices are used as sensors. To date, most of the models developed have been restricted to the weak-probe regime. However, fulfilling the weak-probe power constraint may not always be easy, desired or necessary. Here we present a model for simulating the spectra of alkali-metal vapours for a variety of experimental parameters, most distinctly at intensities beyond weak laser fields. The model incorporates optical pumping effects and transit-time broadening. We test the performance of the model by performing spectroscopy of 87Rb in a magnetic field of 0.6 T, where isolated atomic resonances can be addressed. We find very good agreement between the model and data for three different beam diameters and a variation of intensity of over five orders of magnitude. The non-overlapping absorption lines allow us to differentiate the saturation behaviour of open and closed transitions. While our model was only experimentally verified for the D2 line of rubidium, the software is also capable of simulating spectra of rubidium, sodium, potassium and caesium over both D lines.