Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

New Journal of Physics

Modelling spectra of hot alkali vapour in the saturation regime

Daniel R Häupl, Clare R. Higgins, Danielle Pizzey, Jack D. Briscoe, Steven A. Wrathmall, Ifan G. Hughes, Robert Löw, Nicolas Y. Joly

Published Feb 18, 2025• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/adb77c

Related papers

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 Physics•Jul 5, 2022•16 citations

Optical pumping spectroscopy of Rb vapour with co-propagating laser beams: line identification by a simple theoretical model

Aleksandar J. Krmpot, Mihailo D. Rabasović, Branislav M. Jelenkovic

In this paper the saturation spectra of rubidium vapour at room temperature, obtained with overlapped co-propagating laser beams, were examined. Unlike the standard saturation spectroscopy, here the transmission of the pump laser beam was detected. The pump laser was locked to an atomic transition of the D2 line, while the probe laser frequency was scanned in a wide frequency range. The pump and probe beams had approximately the same intensities; thus the probe laser can saturate transitions and contribute to optical pumping. This, together with Doppler broadening, leads to rich pump transmission spectra, with many lines appearing due to the interaction of lasers with atoms in different velocity groups. The advantages of this method are well-resolved structures and appearance of spectral lines on a flat, Doppler-free background. Agreement between experimental and theoretical results shows the usefulness of this simple model, based on the rate equations, for identification of lines and determination of relative contribution to the observed line intensity from atoms with different velocities. Theoretical spectra are a useful tool for the calibration of experimental spectra obtained by a nonlinear dependence of the laser frequency on the voltage applied to the piezo used for the laser diode frequency scanning.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 14, 2010•5 citations

Applications of the Faraday effect in hot atomic vapours

Mark A. Zentile

This thesis presents both a computational and experimental investigation into light propagation in hot alkali-metal vapours, with a particular focus on utilizing the Faraday effect for practical applications. A model to calculate various spectra for a weak-probe laser beam in an atomic medium with an applied axial magnetic field is presented. A computer program (ElecSus) was developed which implements this model efficiently. Using ElecSus we design optical devices such as Faraday filters and laser frequency stabilizing references. The design of Faraday filters utilizing compact vapour cells is shown, along with excellent agreement with experiment. The importance of including the effect of self broadening in the model is shown for these short path length vapour cells. Also, a Faraday filter is presented that can potentially be used for quantum optics experiments on the caesium D$_1$ line (894~nm). The filter displays the highest ratio of transmission to equivalent noise bandwidth to date for a linear Faraday filter, demonstrating the power of computerized optimization for this application. Furthermore, a Faraday filter is presented for use as an intra-cavity element in an external-cavity diode laser. A proof-of-principle experiment is demonstrated which shows that using a short external cavity with the Faraday filter eliminates mode-hops. Experimentally and theoretically the Faraday effect is investigated in large magnetic fields where alkali-metal atoms enter the hyperfine Paschen-Back regime. This hyperfine Paschen-Back Faraday effect is shown to allow a direct measure of the refractive indices for left and right circular polarized light. Furthermore, fitting the weak-probe spectra using ElecSus is found to give measures of the magnetic field with a fractional precision of the order of $10^{-4}$. In addition we study slow-light pulse propagation in a high density rubidium vapour, showing that our theoretical model for the electric susceptibility is valid for short pulses as well as continuous-wave light. This shows that the model is accurate for predicting weak-probe pulse propagation.

•Jan 1, 2015•4 citations

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

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

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.

arXiv:0805.1139•Journal of Physics B Atomic Molecular and Optical Physics•Jul 24, 2008•232 citations

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, 2008•209 citations

Laser spectroscopy of hot atomic vapours: from ’scope to theoretical fit

Danielle Pizzey, Jack D. Briscoe, Fraser D. Logue +3 more

Abstract The spectroscopy of hot atomic vapours is a hot topic. Many of the work-horse techniques of contemporary atomic physics were first demonstrated in hot vapours. Alkali-metal atomic vapours are ideal media for quantum-optics experiments as they combine: a large resonant optical depth; long coherence times; and well-understood atom–atom interactions. These features aid with the simplicity of both the experimental set up and the theoretical framework. The topic attracts much attention as these systems are ideal for studying both fundamental physics and has numerous applications, especially in sensing electromagnetic fields and quantum technology. This tutorial reviews the necessary theory to understand the Doppler broadened absorption spectroscopy of alkali-metal atoms, and explains the data taking and processing necessary to compare theory and experiment. The aim is to provide a gentle introduction to novice scientists starting their studies of the spectroscopy of thermal vapours while also calling attention to the application of these ideas in the contemporary literature. In addition, the work of expert practitioners in the field is highlighted, explaining the relevance of three extensively-used software packages that complement the presentation herein.

New Journal of Physics•Oct 24, 2022•46 citations
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.
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.
In this paper the saturation spectra of rubidium vapour at room temperature, obtained with overlapped co-propagating laser beams, were examined. Unlike the standard saturation spectroscopy, here the transmission of the pump laser beam was detected. The pump laser was locked to an atomic transition of the D2 line, while the probe laser frequency was scanned in a wide frequency range. The pump and probe beams had approximately the same intensities; thus the probe laser can saturate transitions and contribute to optical pumping. This, together with Doppler broadening, leads to rich pump transmission spectra, with many lines appearing due to the interaction of lasers with atoms in different velocity groups. The advantages of this method are well-resolved structures and appearance of spectral lines on a flat, Doppler-free background. Agreement between experimental and theoretical results shows the usefulness of this simple model, based on the rate equations, for identification of lines and determination of relative contribution to the observed line intensity from atoms with different velocities. Theoretical spectra are a useful tool for the calibration of experimental spectra obtained by a nonlinear dependence of the laser frequency on the voltage applied to the piezo used for the laser diode frequency scanning.
This thesis presents both a computational and experimental investigation into light propagation in hot alkali-metal vapours, with a particular focus on utilizing the Faraday effect for practical applications. A model to calculate various spectra for a weak-probe laser beam in an atomic medium with an applied axial magnetic field is presented. A computer program (ElecSus) was developed which implements this model efficiently. Using ElecSus we design optical devices such as Faraday filters and laser frequency stabilizing references. The design of Faraday filters utilizing compact vapour cells is shown, along with excellent agreement with experiment. The importance of including the effect of self broadening in the model is shown for these short path length vapour cells. Also, a Faraday filter is presented that can potentially be used for quantum optics experiments on the caesium D1_11​ line (894~nm). The filter displays the highest ratio of transmission to equivalent noise bandwidth to date for a linear Faraday filter, demonstrating the power of computerized optimization for this application. Furthermore, a Faraday filter is presented for use as an intra-cavity element in an external-cavity diode laser. A proof-of-principle experiment is demonstrated which shows that using a short external cavity with the Faraday filter eliminates mode-hops. Experimentally and theoretically the Faraday effect is investigated in large magnetic fields where alkali-metal atoms enter the hyperfine Paschen-Back regime. This hyperfine Paschen-Back Faraday effect is shown to allow a direct measure of the refractive indices for left and right circular polarized light. Furthermore, fitting the weak-probe spectra using ElecSus is found to give measures of the magnetic field with a fractional precision of the order of 10−410^{-4}10−4. In addition we study slow-light pulse propagation in a high density rubidium vapour, showing that our theoretical model for the electric susceptibility is valid for short pulses as well as continuous-wave light. This shows that the model is accurate for predicting weak-probe pulse propagation.
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 The spectroscopy of hot atomic vapours is a hot topic. Many of the work-horse techniques of contemporary atomic physics were first demonstrated in hot vapours. Alkali-metal atomic vapours are ideal media for quantum-optics experiments as they combine: a large resonant optical depth; long coherence times; and well-understood atom–atom interactions. These features aid with the simplicity of both the experimental set up and the theoretical framework. The topic attracts much attention as these systems are ideal for studying both fundamental physics and has numerous applications, especially in sensing electromagnetic fields and quantum technology. This tutorial reviews the necessary theory to understand the Doppler broadened absorption spectroscopy of alkali-metal atoms, and explains the data taking and processing necessary to compare theory and experiment. The aim is to provide a gentle introduction to novice scientists starting their studies of the spectroscopy of thermal vapours while also calling attention to the application of these ideas in the contemporary literature. In addition, the work of expert practitioners in the field is highlighted, explaining the relevance of three extensively-used software packages that complement the presentation herein.