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

Applied Physics Letters

Optically end-pumped scheme in rubidium vapor: Theory and experiment

Chenxu Liu, Yalong Hai, Anhong Dang

Published Sep 5, 2022• 2 citations
Publisher

Abstract

The optimal detuning of the pump light at the rubidium D2 line is calculated and experimentally validated. A three-level optically end-pumped model in a hot rubidium vapor cell is demonstrated, which takes into account the hyperfine structure of the ground state, various collisional processes, and the nonlinear absorption of the pump light along the cell length. By developing a constrained optimization model, we calculate the optimal detuning of the pump light that maximizes the average excited state atom concentration in the cell. Experimentally, a 1529 nm probe light at higher levels, which is attenuated to the weak-probe limit, is introduced to accurately characterize the excited state atom concentration. Coupling with the experimental results, the variation of the pump light optimal detuning with the temperature and the pump light intensity at the unsaturated pumping is analyzed. At the optimal detuning point, the theoretical decay function of the pump light percentage along the vapor cell length almost coincides regardless of the temperature and the pump light intensity changes. Moreover, the theoretical fitted pump light decay function at optimal detuning is predicted. The fitted pump light percentage exiting the vapor cell is 4.75%. A fast implementation method to achieve the maximal average excited state atom concentration in the experiment is demonstrated.

DOI
10.1063/5.0108245

Related papers

Single-Photon-Level Sub-Doppler Pump-Probe Spectroscopy of Rubidium

Paul Burdekin, Samuele Grandi, Rielly Newbold +3 more

We propose and demonstrate pump-probe spectroscopy of rubidium absorption that reveals the sub-Doppler hyperfine structure of the ${}^{5}{\mathrm{S}}_{1/2}\ensuremath{\leftrightarrow}{}^{5}{\mathrm{P}}_{3/2}$ (${\mathrm{D}}_{2}$) transitions. The counterpropagating pump and probe lasers are independently tunable in frequency, with the probe operating at the single-photon level. The two-dimensional spectrum measured as the laser frequencies are scanned shows fluorescence, Doppler-broadened absorption dips, and sub-Doppler features. The detuning between the pump and probe lasers allows compensation of the Doppler shift for all atomic velocities in the room-temperature vapor, meaning we observe sub-Doppler features for all atoms in the beam. We detail a theoretical model of the system that incorporates fluorescence, saturation effects, and optical pumping and compare this with the measured spectrum, finding a mean absolute percentage error of 3.11%. This high level of agreement allows us to extract the number density and temperature of the $\mathrm{Rb}$ vapor from the two-dimensional spectrum. In the future this technique could be used as an atomic frequency standard for calibrating and characterising a single-photon or low-light-level source.

arXiv:2007.08452•Physical Review Applied•Oct 23, 2020•9 citations

Semiclassical calculation of the power saturation of the Kerr effect in Rb vapor. II: the effect of incomplete optical pumping

Zachary H. Levine

Rubidium vapor cells play a key role in contemporary quantum optics since they have strong nonlinear interactions with a low-power incident laser light. The simplest nonlinear interaction is the Kerr effect. Although most calculations concentrate on the unsaturated Kerr effect, the saturated Kerr effect has been measured in many materials including 85Rb and 87Rb vapor. Moreover, entanglement-generating vapor cells often operate in the saturated regime. Here, the calculation of the saturated Kerr effect for rubidium vapor at the D2 line uses a density matrix formulation that includes two hyperfine-split levels and all magnetic sublevels in each of the ground and excited states to account for incomplete optical pumping: the transit time of the atoms through the beam is too short to reach a final population distribution. The calculation shows a rapid qualitative change at low optical power, in semiquantitative agreement with experimental data.

Journal of the Optical Society of America B•Apr 24, 2025•1 citation

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

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

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

Determining the Two-Photon Absorption Cross-Section for the 52S1/2 --> 52D5/2 Transition in Naturally Occurring Rubidium

Jeffrey Gallagher, Glen P. Perram

Recently we demonstrated lasing at 420 nm and 455 nm inside of rubidium and cesium vapor cells respectively, by non-resonant, two photon absorption at near infrared pump wavelengths. Two photon absorption from the ground S1/2 state to excited D3/2,5/2 or higher lying S1/2 state via virtual states and subsequent infrared stimulated emission pumps the upper laser levels, the second excited P1/2,3/2 states. To better understand the mechanism and phenomenology of this type of laser, this paper presents a method for determining the two-photon absorption (TPA) cross-section for the 5S1/2 −→ 5D5/2 transition in naturally occurring rubidium. For an incident pump intensity of 392 W cm2 and a rubidium concentration of 3.34 × 10 atoms cm3 , a peak absorbance of 0.10 is observed. The concentration of the Rb in the test cell is determined by one photon absorption spectra of the D2, indicating a vapor curve shifted by 14 C from the exterior wall temperature. The incident laser beam is focused to a waist of 75 μm. The beam quality is consistent with an M = 1.05 − 1.09. A model for the intensity as a function of propagation distance is developed to interpret the observed absorption spectrum and determine a cross-section for the two photon absorption.

AIAA Plasmadynamics and Lasers Conference•Jun 1, 2011•1 citation
The optimal detuning of the pump light at the rubidium D2 line is calculated and experimentally validated. A three-level optically end-pumped model in a hot rubidium vapor cell is demonstrated, which takes into account the hyperfine structure of the ground state, various collisional processes, and the nonlinear absorption of the pump light along the cell length. By developing a constrained optimization model, we calculate the optimal detuning of the pump light that maximizes the average excited state atom concentration in the cell. Experimentally, a 1529 nm probe light at higher levels, which is attenuated to the weak-probe limit, is introduced to accurately characterize the excited state atom concentration. Coupling with the experimental results, the variation of the pump light optimal detuning with the temperature and the pump light intensity at the unsaturated pumping is analyzed. At the optimal detuning point, the theoretical decay function of the pump light percentage along the vapor cell length almost coincides regardless of the temperature and the pump light intensity changes. Moreover, the theoretical fitted pump light decay function at optimal detuning is predicted. The fitted pump light percentage exiting the vapor cell is 4.75%. A fast implementation method to achieve the maximal average excited state atom concentration in the experiment is demonstrated.
We propose and demonstrate pump-probe spectroscopy of rubidium absorption that reveals the sub-Doppler hyperfine structure of the ${}^{5}{\mathrm{S}}_{1/2}\ensuremath{\leftrightarrow}{}^{5}{\mathrm{P}}_{3/2}$ (D2{\mathrm{D}}_{2}D2​) transitions. The counterpropagating pump and probe lasers are independently tunable in frequency, with the probe operating at the single-photon level. The two-dimensional spectrum measured as the laser frequencies are scanned shows fluorescence, Doppler-broadened absorption dips, and sub-Doppler features. The detuning between the pump and probe lasers allows compensation of the Doppler shift for all atomic velocities in the room-temperature vapor, meaning we observe sub-Doppler features for all atoms in the beam. We detail a theoretical model of the system that incorporates fluorescence, saturation effects, and optical pumping and compare this with the measured spectrum, finding a mean absolute percentage error of 3.11%. This high level of agreement allows us to extract the number density and temperature of the Rb\mathrm{Rb}Rb vapor from the two-dimensional spectrum. In the future this technique could be used as an atomic frequency standard for calibrating and characterising a single-photon or low-light-level source.
Rubidium vapor cells play a key role in contemporary quantum optics since they have strong nonlinear interactions with a low-power incident laser light. The simplest nonlinear interaction is the Kerr effect. Although most calculations concentrate on the unsaturated Kerr effect, the saturated Kerr effect has been measured in many materials including 85Rb and 87Rb vapor. Moreover, entanglement-generating vapor cells often operate in the saturated regime. Here, the calculation of the saturated Kerr effect for rubidium vapor at the D2 line uses a density matrix formulation that includes two hyperfine-split levels and all magnetic sublevels in each of the ground and excited states to account for incomplete optical pumping: the transit time of the atoms through the beam is too short to reach a final population distribution. The calculation shows a rapid qualitative change at low optical power, in semiquantitative agreement with experimental data.
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 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.
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.
Recently we demonstrated lasing at 420 nm and 455 nm inside of rubidium and cesium vapor cells respectively, by non-resonant, two photon absorption at near infrared pump wavelengths. Two photon absorption from the ground S1/2 state to excited D3/2,5/2 or higher lying S1/2 state via virtual states and subsequent infrared stimulated emission pumps the upper laser levels, the second excited P1/2,3/2 states. To better understand the mechanism and phenomenology of this type of laser, this paper presents a method for determining the two-photon absorption (TPA) cross-section for the 5S1/2 −→ 5D5/2 transition in naturally occurring rubidium. For an incident pump intensity of 392 W cm2 and a rubidium concentration of 3.34 × 10 atoms cm3 , a peak absorbance of 0.10 is observed. The concentration of the Rb in the test cell is determined by one photon absorption spectra of the D2, indicating a vapor curve shifted by 14 C from the exterior wall temperature. The incident laser beam is focused to a waist of 75 μm. The beam quality is consistent with an M = 1.05 − 1.09. A model for the intensity as a function of propagation distance is developed to interpret the observed absorption spectrum and determine a cross-section for the two photon absorption.