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

^{87}\mathrm{Rb}

DOI: 10.1103/physreva.91.053423

Related papers

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

Hai Truong Nguyen, Goga Veshapedze, Chris Verzani +3 more

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 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.

Bulletin of the American Physical SocietyJun 4, 20142 citations

Model-independent measurement of the excited fraction in a magneto-optical trap

M. H. Shah, H. A. Camp, M. L. Trachy +3 more

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 $^{87}\mathrm{Rb}$ 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 $^{87}\mathrm{Rb}$ 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.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 $^{87}\mathrm{Rb}$ 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 $^{87}\mathrm{Rb}$ 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.

Physical Review AMay 31, 200735 citations

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

Jonathan M. Kwolek, D. S. Goodman, Samuel Entner +3 more

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.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.

arXiv:1802.05306Physical Review AMay 31, 201811 citations

Determination of the atom’s excited-state fraction in a magneto-optical trap

Yue Guo Shen

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.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.

Jan 1, 20180 citations

Bichromatic magneto-optical trapping for J→J,J−1 configurations

Anne Cournol, P. Pillet, Hans Lignier +1 more

A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$ transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the $J\ensuremath{\rightarrow}J\ensuremath{-}1$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0$) and $J\ensuremath{\rightarrow}J$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1/2\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=1/2$). A one-dimensional (1D) model is presented and a complete 3D simulation using rate equations confirms the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the ${\mathrm{C}}_{2}^{\ensuremath{-}}$ molecular anion as a typical example of the interplay between the two simple transitions $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$.A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$ transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the $J\ensuremath{\rightarrow}J\ensuremath{-}1$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0$) and $J\ensuremath{\rightarrow}J$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1/2\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=1/2$). A one-dimensional (1D) model is presented and a complete 3D simulation using rate equations confirms the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the ${\mathrm{C}}_{2}^{\ensuremath{-}}$ molecular anion as a typical example of the interplay between the two simple transitions $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$.

arXiv:1605.06464Physical Review AMay 24, 20163 citations

Photon-scattering-rate measurement of atoms in a magneto-optical trap

Kais Jooya, Nam Musterer, Kirk W. Madison +1 more

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.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.

Physical Review ADec 2, 20139 citations

^{85}\mathrm{Rb}

^{87}\mathrm{Rb}

Model-Free Measurement of the Excited-State Fraction in a

^{85}

Rb Magneto-Optical Trap

^{87}\mathrm{Rb}

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

^{87}\mathrm{Rb}

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.