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Bulletin of the American Physical Society

Model-Free Measurement of the Excited-State Fraction in a $^{85}$Rb Magneto-Optical Trap

Hai Truong Nguyen, Goga Veshapedze, Chris Verzani, Charles Fehrenbach, J. Bang, Brett D DePaola

Published Jun 4, 2014• 2 citations
OpenAlex

Abstract

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.

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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.
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.
In many experiments involving a magneto-optical trap (MOT) it is of great importance to know the fraction of atoms placed in an excited state due to the trapping process. Generally speaking, researchers have had to use overly simplistic and untested models to estimate this fraction. In this work, the excited fractions of 87Rb^{87}\mathrm{Rb}87Rb atoms in a MOT are directly measured using a charge transfer technique, for a range of MOT parameters. Simple models are then fit to the measured fractions. Using the results of this work, the excited fraction of 87Rb^{87}\mathrm{Rb}87Rb atoms trapped in a MOT can be accurately estimated with knowledge of only the trapping laser intensity and detuning. The results are, at most, only weakly dependent on other MOT parameters.
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.
This thesis introduces an empirical method for determining and controlling the excited-state fraction of atoms in a magneto-optical trap (MOT), which is essential for the use of cold atoms as a sensor when they are held in a MOT since their interactions with other particles and fields are quantum state dependent. A four-level theoretical atomic model was used to describe the transitions of the atoms in a MOT, and the fluorescence emitted from a fixed number of atoms under different laser conditions were measured to determine the saturation parameters empirically. Two saturation parameters P_sat= 1.15 (0.06) mW and P_r,sat= 2.05 (0.59) mW were successfully extracted from the model, and the excited-state fraction in the four-level model was accurately calculated as a function of the MOT trap parameters, which ranges from 0.045 to 0.415 for the experimental settings currently available. We also observed minor deviations from the four-level model for the photon scattering rate, and a hypothesis of atom pinning under high powers was proposed to explain the problem. We plan to use this simple excited-state fraction determination method to distinguish the ground and excited state collision cross section of Rubidium atoms with species in residual gas of the vacuum. This is the first step to establishing atom loss rates from a MOT as an atomic primary pressure standard.
We study several magneto-optical trapping configurations in 87Rb^{87}\mathrm{Rb}87Rb. These unconventional MOTs all use type-II transitions, where the angular momentum of the ground state is greater than or equal to that of the excited state. Some use red-detuned light, and others blue-detuned light. The properties of these MOTs are strongly influenced by the balance between opposing Doppler and Sisyphus forces, and vary widely from one configuration to another. In the blue-detuned MOT, Sisyphus cooling dominates over Doppler heating for all relevant speeds and magnetic fields. We measure the capture velocity of this MOT as a function of intensity and detuning, finding a maximum of $3.8\ifmmode\pm\else\textpm\fi{}0.1$ m/s. Atomic densities are particularly high in the blue-detuned MOT, and its lifetime is limited by collisions between the trapped atoms. We present measurements of the loss rate due to these ultracold collisions as a function of laser intensity and detuning. In the red-detuned MOTs, Sisyphus heating dominates at low speeds and Doppler cooling at higher speeds. Consequently, temperatures in the red-detuned MOTs are up to a thousand times higher than in the blue-detuned MOTs. One MOT forms large ring structures, with no density at the center, showing how atoms driven towards a non-zero equilibrium speed remain trapped by orbiting around the center. Another MOT demonstrates that magnetic mixing of the excited-state hyperfine levels can be an important mechanism in type-II MOTs.
We present a technique for empirically determining the photon scattering rate of atoms in a magneto-optical trap (MOT). An accurate measurement of the scattering rate provides a way to accurately determine the number of atoms in the MOT, the excited-state fraction, and the in situ light intensity experienced by the atoms in the trap. We validate this technique for determining the scattering rate by comparing the atom number determined by the fluorescence emitted by atoms in a MOT with an independent and unrelated measure of the number determined by an absorption measurement of an optical pumping beam. We also observe minor deviations from the two-level model for the single-photon scattering rate and extend our analysis to a four-level model. The main advantage of the method described here is that it provides a simple way of determining the photon scattering rate of the MOT empirically and, thus, of evaluating the atom number from fluorescence measurements more accurately.