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arXiv:1802.05306 · Physical Review A

Model-independent measurements of the sodium magneto-optical trap's excited-state population

Jonathan M. Kwolek, D. S. Goodman, Samuel Entner, James E. Wells, Frank A. Narducci, W. W. Smith

Published May 31, 2018• 11 citations
arXivHTMLPDF

Abstract

We present model-independent measurements of the excited-state population of atoms in a sodium (Na) magneto-optical trap (MOT) using a hybrid ion-neutral trap composed of a MOT and a linear Paul trap (LPT). We photoionize excited Na atoms trapped in the MOT and use two independent methods to measure the resulting ions: directly by trapping them in our LPT, and indirectly by monitoring changes in MOT fluorescence. By measuring the ionization rate via these two independent methods, we have enough information to directly determine the population of MOT atoms in the excited state. The resulting measurement reveals that there is a range of trapping-laser intensities where the excited-state population of atoms in our MOT follows the standard two-level model intensity dependence. However, an experimentally determined effective saturation intensity must be used instead of the theoretically predicted value from the two-level model. We measured the effective saturation intensity to be ${I}_{\mathrm{SE}}=22.9\ifmmode\pm\else\textpm\fi{}5.1\phantom{\rule{0.222222em}{0ex}}\mathrm{mW}/{\mathrm{cm}}^{2}$ for the type-I Na MOT and ${I}_{\mathrm{SE}}=49\ifmmode\pm\else\textpm\fi{}11\phantom{\rule{0.28em}{0ex}}\mathrm{mW}/{\mathrm{cm}}^{2}$ for the type-II Na MOT, approximately 1.7 and 3.6 times the theoretical estimate, respectively. Lastly, at large trapping-laser intensities, our experiment reveals a clear departure from the two-level model at a critical intensity that we believe is due to a state-mixing effect, the critical intensity of which can be determined by a simple power broadening model.

DOI
10.1103/physreva.97.053420

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Bulletin of the American Physical Society•Jun 4, 2014•2 citations
We present model-independent measurements of the excited-state population of atoms in a sodium (Na) magneto-optical trap (MOT) using a hybrid ion-neutral trap composed of a MOT and a linear Paul trap (LPT). We photoionize excited Na atoms trapped in the MOT and use two independent methods to measure the resulting ions: directly by trapping them in our LPT, and indirectly by monitoring changes in MOT fluorescence. By measuring the ionization rate via these two independent methods, we have enough information to directly determine the population of MOT atoms in the excited state. The resulting measurement reveals that there is a range of trapping-laser intensities where the excited-state population of atoms in our MOT follows the standard two-level model intensity dependence. However, an experimentally determined effective saturation intensity must be used instead of the theoretically predicted value from the two-level model. We measured the effective saturation intensity to be ISE=22.9\ifmmode±\else\textpm\fi5.1mW/cm2{I}_{\mathrm{SE}}=22.9\ifmmode\pm\else\textpm\fi{}5.1\phantom{\rule{0.222222em}{0ex}}\mathrm{mW}/{\mathrm{cm}}^{2}ISE​=22.9\ifmmode±\else\textpm\fi5.1mW/cm2 for the type-I Na MOT and ISE=49\ifmmode±\else\textpm\fi11mW/cm2{I}_{\mathrm{SE}}=49\ifmmode\pm\else\textpm\fi{}11\phantom{\rule{0.28em}{0ex}}\mathrm{mW}/{\mathrm{cm}}^{2}ISE​=49\ifmmode±\else\textpm\fi11mW/cm2 for the type-II Na MOT, approximately 1.7 and 3.6 times the theoretical estimate, respectively. Lastly, at large trapping-laser intensities, our experiment reveals a clear departure from the two-level model at a critical intensity that we believe is due to a state-mixing effect, the critical intensity of which can be determined by a simple power broadening model.
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We present measurements of the total elastic and resonant charge-exchange ion-atom collision rate coefficient kia{k}_{\mathrm{ia}}kia​ of cold sodium (Na) with optically dark low-energy Na+{\mathrm{Na}}^{+}Na+ ions in a hybrid ion-neutral trap. To determine kia{k}_{\mathrm{ia}}kia​, we measured the trap loading and loss rates from both a Na magneto-optical trap (MOT) and a linear radio-frequency quadrupole Paul trap. We found the total rate coefficient to be $7.4\ifmmode\pm\else\textpm\fi{}1.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{3}/\mathrm{s}$ for the type-I Na MOT immersed within an $\ensuremath{\approx}140\ensuremath{-}\mathrm{K}$ ion cloud and $1.10\ifmmode\pm\else\textpm\fi{}0.25\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{3}/\mathrm{s}$ for the type-II Na MOT within an $\ensuremath{\approx}1070\ensuremath{-}\mathrm{K}$ ion cloud. Our measurements show excellent agreement with previously reported theoretical fully quantal ab initio calculations. In the process of determining the total rate coefficient, we demonstrate that a MOT can be used to probe an optically dark ion cloud's spatial distribution within a hybrid trap.
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We present measurements of the charge-exchange reaction rate between neutral sodium (Na) and ionized calcium (Ca+{\mathrm{Ca}}^{+}Ca+) in a hybrid atom-ion trap, which is comprised of a Na magneto-optical trap concentric with a linear Paul trap. Once the Na and Ca+{\mathrm{Ca}}^{+}Ca+ are co-trapped, the reaction rate is measured by continuously quenching the reaction product Na+{\mathrm{Na}}^{+}Na+ from the ion trap, and then destructively measuring the decay of the remaining ion population. The reactants' electronic state and temperature are experimentally controlled, allowing us to determine the four individual reaction rates between Na[SorP]\text{Na}[S\phantom{\rule{4.pt}{0ex}}\text{or}\phantom{\rule{4.pt}{0ex}}P]Na[SorP] and Ca+[SorD]{\text{Ca}}^{+}[S\phantom{\rule{4.pt}{0ex}}\text{or}\phantom{\rule{4.pt}{0ex}}D]Ca+[SorD] at different collision energies. With the exception of the largest reaction-rate channel (Na[P]+Ca+[D]\text{Na}[P]+{\text{Ca}}^{+}[D]Na[P]+Ca+[D]), our rates are consistent with the classical Langevin rate limit. We have also found evidence of reactant collision-energy thresholds associated with two of the four entrance channels.
In many experiments involving magneto-optical traps (MOTs), it is imperative to know the fraction of atoms left in an excited state by the cooling and trapping lasers. In most cases, researchers have used formulas that were derived for simple two-level systems interacting with a single beam of light having a well-defined polarization, and in the absence of magnetic or electric fields. However, a MOT environment is much more complex than this. Here we directly measure the excited fraction in a MOT of 85Rb^{85}\mathrm{Rb}85Rb atoms in a model-independent manner for a wide range of trapping conditions. We then fit our measured fractions to an ansatz based on a simple model. Knowing only the trapping laser's total intensity and detuning from resonance, one can then use this ansatz to accurately predict the excited fraction. The work is a companion piece to similar measurements on a MOT of 87Rb^{87}\mathrm{Rb}87Rb.
Model-Free Measurement of the Excited-State Fraction in a 85^{85}85Rb Magneto-Optical Trap
In many experiments involving magneto-optical traps (MOTs), it is imperative to know the fraction of atoms left in an excited state by the cooling and trapping lasers. In most cases, researchers have used formulas that were derived for simple 2-level systems interacting with a single beam of light having a well-defined polarization, and in the absence of magnetic or electric fields. However a MOT environment is much more complex than this. Here we directly measure the excited fraction in a MOT of 85Rb atoms in a model-independent manner for a wide range of trapping conditions. We then fit our measured fractions to an ansatz based on a simple model. Knowing only the trapping laser's total intensity and detuning from resonance, one can then use this ansatz to accurately predict the excited fraction. The work is a companion piece to similar measurements on a MOT of 87Rb.