arXiv:0805.1139 · Journal of Physics B Atomic Molecular and Optical Physics

Absolute absorption on rubidium D lines: comparison between theory and experiment

Paul Siddons, Charles S. Adams, Chang Ge, Ifan G. Hughes

Published Jul 24, 2008• 232 citations

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 degrees C.

DOI: 10.1088/0953-4075/41/15/155004

Related papers

Absolute absorption on rubidium D lines: comparison between theory and experiment

Paul Siddons, Charles S. Adams, Chang Ge +1 more

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.

Jan 1, 2008209 citations

A comprehensive model for Doppler spectra in thermal atomic vapour

Rajni Bala, Joyee Ghosh, Vivek Venkataraman

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.

Journal of Physics B Atomic Molecular and Optical PhysicsJul 5, 202216 citations

Absolute absorption on the potassium D lines: theory and experiment

R Hanley, Philip D Gregory, Ifan G. Hughes +1 more

Abstract We present a detailed study of the absolute Doppler-broadened absorption of a probe beam scanned across the potassium D lines in a thermal vapour. Spectra using a weak probe were measured on the 4S 4P transition and compared to the theoretical model of the electric susceptibility detailed by Zentile et al (2015 Comput. Phys. Commun. 189 162–74 ) in the code named ElecSus. Comparisons were also made on the 4S 5P transition with an adapted version of ElecSus. This is the first experimental test of ElecSus on an atom with a ground state hyperfine splitting smaller than that of the Doppler width. An excellent agreement was found between ElecSus and experimental measurements at a variety of temperatures with rms errors . We have also demonstrated the use of ElecSus as an atomic vapour thermometry tool, and present a possible new measurement technique of transition decay rates which we predict to have a precision of ∼ .

arXiv:1506.06651Journal of Physics B Atomic Molecular and Optical PhysicsAug 28, 201529 citations

Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen-Back regime

Weller, L, Kleinbach, KS, Zentile, MA +4 more

Here we report on measurements of the absolute absorption and dispersion properties of an isotopically pure 87Rb vapour for magnetic fields up to and including 0.6 T. We discuss the various regimes that arise when the hyperfine and Zeeman interactions have different magnitudes, and show that we enter the hyperfine Paschen–Back regime for fields greater than 0.33 T on the Rb D2 line. The experiment uses a compact 1 mm3 microfabricated vapour cell that makes it easy to maintain a uniform and large magnetic field with a small and inexpensive magnet. We find excellent agreement between the experimental results and numerical calculations of the weak probe susceptibility where the line positions and strengths are calculated by matrix diagonalization.

Nov 14, 201244 citations

Absolute absorption on the rubidium D 1 line including resonant dipole–dipole interactions

Lee Weller, Robert J. Bettles, Paul Siddons +2 more

Here we report on measurements of the absolute absorption spectra of dense rubidium vapour on the D 1 line in the weak-probe regime for temperatures up to 170 °C and number densities up to 3 × 10 14 cm −3 . In such vapours, modifications to the homogeneous linewidth of optical transitions arise due to dipole–dipole interactions between identical atoms, in superpositions of the ground and excited states. Absolute absorption spectra were recorded with a deviation of 0.1% between experiment and a theory incorporating resonant dipole–dipole interactions. The manifestation of dipole–dipole interactions is a self-broadening contribution to the homogeneous linewidth, which grows linearly with number density of atoms. Analysis of the absolute absorption spectra allows us to ascertain the value of the self-broadening coefficient for the rubidium D 1 line: β/2π = (0.69 ± 0.04) × 10 −7 Hz cm 3 , in excellent agreement with the theoretical prediction.

arXiv:1107.3092Journal of Physics B Atomic Molecular and Optical PhysicsSep 1, 2011100 citations

Modelling spectra of hot alkali vapour in the saturation regime

Daniel R Häupl, Clare R. Higgins, Danielle Pizzey +5 more

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.

New Journal of PhysicsFeb 18, 20254 citations