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Physical Review A

Optical pumping with two finite linewidth lasers

Pierre‐Luc Tremblay, Claude Jacques

Published May 1, 1990• 48 citations
Publisher

Abstract

Two-laser optical pumping schemes show great promise for atom preparation since they can act as a nearly perfect state selector. This paper presents a new theoretical model to evaluate the pumping efficiency of two-laser pumping schemes, taking into account optical, ground and excited states hyperfine and Zeeman coherences, neighboring transitions, and fluctuating laser fields. The model is used to predict the optical pumping efficiency of two lasers with Lorentzian spectral profiles on a beam of cesium atoms. The particular laser intensities and linewidths that optimize the optical pumping efficiency and rate are calculated.

DOI
10.1103/physreva.41.4989

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Physical Chemistry Chemical Physics•Jan 1, 2025•0 citations
Two-laser optical pumping schemes show great promise for atom preparation since they can act as a nearly perfect state selector. This paper presents a new theoretical model to evaluate the pumping efficiency of two-laser pumping schemes, taking into account optical, ground and excited states hyperfine and Zeeman coherences, neighboring transitions, and fluctuating laser fields. The model is used to predict the optical pumping efficiency of two lasers with Lorentzian spectral profiles on a beam of cesium atoms. The particular laser intensities and linewidths that optimize the optical pumping efficiency and rate are calculated.
In this paper the optical pumping of a cesium beam is investigated. The rate equation model is used to calculate the population difference created by laser diode(s) illuminating the beam. The finite laser and atomic linewidths are taken into account in order to analyze leakage effects on neighboring transitions. One-laser and two-laser pumping is considered and the best-suited two-laser configurations for preparing the cesium atoms in a single mF{m}_{F}mF​=0 sublevel are specified. Experimental results on both the leakage effect and the population difference achieved agree with theoretical predictions.
This paper presents a theoretical analysis of a possible scheme to realize a strong population difference between the two ground state sub-levels F = 4, MF = 0, and F = 3, MF = 0 of caesium atom. Two laser-diode light beams, π polarized, are used to illuminate at right angle an atomic beam. The efficiency of the population difference build up is evaluated for two limiting cases according to the light spectral distribution : the monochromatic and broadband excitations. This analysis takes into account hyperfine and Zeeman structures of the energy levels. Numerical calculations show that the monochromatic excitation leads to steady state population difference close to the value obtained with a single pumping laser; however all the atoms can be brought in the upper level if the two laser lights are considered broadband and uncorrelated Guidelines are derived to obtain an efficient optically pumped caesium beam frequency standard.
We use two-laser optical pumping on a continuous atomic fountain in order to prepare cold cesium atoms in the same quantum ground state. A first laser excites the F=4F=4F=4 ground state to pump the atoms toward F=3F=3F=3 while a second $\ensuremath{\pi}$-polarized laser excites the $F=3\ensuremath{\rightarrow}{F}^{'}=3$ transition of the D2{D}_{2}D2​ line to produce Zeeman pumping toward m=0m=0m=0. To avoid trap states, we implement the first laser in a two-dimensional optical lattice geometry, thereby creating polarization gradients. This configuration has the advantage of simultaneously producing Sisyphus cooling when the optical lattice laser is tuned between the $F=4\ensuremath{\rightarrow}{F}^{'}=4$ and $F=4\ensuremath{\rightarrow}{F}^{'}=5$ transitions of the D2{D}_{2}D2​ line, which is important to remove the heat produced by optical pumping. Detuning the frequency of the second $\ensuremath{\pi}$-polarized laser reveals the action of a mechanism improving both laser cooling and state-preparation efficiency. A physical interpretation of this mechanism is discussed.
The D1 line spectrally selective pumping process in Doppler-broadened cesium is analyzed by solving the optical Bloch equations. The process, described by a three-level model with the Λ scheme, shows that the saturation intensity of broadened atoms is three orders of magnitude larger than that of resting atoms. The |Fg = 3〉 → |Fe = 4〉 resonance pumping can result in the ground state |Fg = 4, mF = 4〉 sublevel having a maximum population of 0.157 and the population difference would be about 0.01 in two adjacent magnetic sublevels of the hyperfine (HF) state Fg = 4. To enhance the anisotropy in the ground state, we suggest employing dichromatic optical HF pumping by adding a laser to excite D1 line |Fg = 4〉 → |Fe = 3〉 transition, in which the cesium magnetometer sensitivity increases by half a magnitude and is unaffected by the nonlinear Zeeman effect even in Earth's average magnetic field.
The D1 line spectrally selective pumping process in Doppler-broadened cesium is analyzed by solving the optical Bloch equations. The process, described by a three-level model with the A scheme, shows that the saturation intensity of broadened atoms is three orders of magnitude larger than that of resting atoms. The 丨Fg = 3） →丨Fe = 4） resonance pumping can result in the ground state丨Fg = 4, mF = 4） sublevel having a maximum population of 0.157 and the population difference would be about 0.01 in two adjacent magnetic sublevels of the hyperfine （HF） state Fg = 4. To enhance the anisotropy in the ground state, we suggest employing dichromatic optical HF pumping by adding a laser to excite D1 line 丨Fg = 4） → 丨Fe = 3） transition, in which the cesium magnetometer sensitivity increases by half a magnitude and is unaffected by the nonlinear Zeeman effect even in Earth＇s average magnetic field.
Cs) atoms by applying circularly polarized light at an optimal frequency for electronic transitions from ground to excited states. To enhance control over sublevel populations following optical pumping, we incorporate a radiofrequency (RF) field. This integrated approach enables us to achieve a tailored distribution of atomic sublevel populations with high efficiency. Utilizing the Lindblad master equation, we provide a comprehensive framework for analyzing these dynamics, examining relaxation rates, repopulation processes, and the evolution of cesium Zeeman sublevels. Our findings underscore the effectiveness of the Lindblad master equation in accounting for external field effects and environmental interactions, significantly improving the accuracy and generalizability of optical pumping models. This method holds substantial promise for various applications in optical experiments, including magnetometry and quantum computing, paving the way for future advancements in these fields.