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A Study of Excited State Atoms in Cold Atom Traps and a test of the Reif Model to Determine Trap Depth.

N. Evetts

Published Jan 1, 2011• 1 citation
Publisher

Abstract

The motivation, theory and applications of atomic traps are briefly reviewed before delving into the primary motivation for the research: the disagreement between theory and experiment for the calculation of trap loss rate constants (< σv >) for Rubidium Magneto-Optical Traps. We use a pure magnetic trap to calibrate for the density of background Rubidium in our system while varying this density and measuring the loss and loading rates for multiple magnetic traps for which the trap depth has been measured previously. This variation of density allows us to infer < σv >, a quantity whose behaviour we attempt to explain in relation to the the excited state fraction of the trapped atoms. We find a strong correlation between the excited state fraction and the loss rate constant which we are, unfortunately, unable to quantify due to data quality issues. In addition to this study, experimental evidence for the confirmation of the Reif Model is provided as well as a new method (based on this model) for measuring the depth of a magneto-optical trap.

DOI
10.14288/1.0085970

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Bulletin of the American Physical Society•May 1, 1993•0 citations
The motivation, theory and applications of atomic traps are briefly reviewed before delving into the primary motivation for the research: the disagreement between theory and experiment for the calculation of trap loss rate constants (< σv >) for Rubidium Magneto-Optical Traps. We use a pure magnetic trap to calibrate for the density of background Rubidium in our system while varying this density and measuring the loss and loading rates for multiple magnetic traps for which the trap depth has been measured previously. This variation of density allows us to infer < σv >, a quantity whose behaviour we attempt to explain in relation to the the excited state fraction of the trapped atoms. We find a strong correlation between the excited state fraction and the loss rate constant which we are, unfortunately, unable to quantify due to data quality issues. In addition to this study, experimental evidence for the confirmation of the Reif Model is provided as well as a new method (based on this model) for measuring the depth of a magneto-optical trap.
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 the dependence of the particle loading rate of a rubidium vapor cell magneto-optic trap (MOT). Using a trap depth determination of the MOT that relies on measurements of loss rates during optical excitation of colliding atoms to a repulsive molecular state, we experimentally determine the MOT escape velocity and show that the loading rate scales with escape velocity to the fourth power, or, equivalently, with the square of the trap depth. We also demonstrate that the loading rate is directly proportional to the background rubidium density. We thus experimentally confirm the loading rate model used in the literature since the invention of the MOT. In addition to confirming this long-standing conjecture, we show that the loading rate dependence can be used to reliably infer the trap depth and to tune the relative depth of a MOT (i.e., capture and escape velocities) when the background density is held fixed. The measurements have allowed an experimental determination of the relationship between capture and escape velocities in our MOTs of vc=1.29(0.12)ve.
A detailed experimental and theoretical investigation of a magneto-optical trap for caesium atoms is presented. Particular emphasis has been placed on achieving high spatial number densities and low temperatures. Optimizing both of these together enables efficient evaporative cooling from a conservative trap, a procedure which has recently led to the first observations of Bose-Einstein condensation in a dilute atomic vapour. The behaviour of a magneto-optical trap is nominally determined by four independent parameters: the detuning and intensity of the light field, the magnetic field gradient and the number of trapped atoms. A model is presented which incorporates previous treatments into a single description of the trap that encompasses a wide range of its behaviour. This model was tested quantitatively by measuring the temperature of the cloud and its spatial distribution as a function of the four parameters. The maximum density was found to be limited both by the reabsorption of photons scattered within the cloud and by a reduction of the confining force at small light shifts. The nonlinear variation with position of the restoring force was found to be significant in limiting the number of atoms confined to a high density. A maximum density in phase space (defined as the number of atoms in a box with sides of dimension one thermal de Broglie wavelength) of (1.5 ± 0.5) x 10-5 was observed, with a spatial density of 1.5 x 1011 atoms per cm3. Cold collision losses from a caesium magneto-optical trap have been studied with the purpose of assessing their influence on spatial densities. In contrast to previous measurements of similar quantities, these measurements did not require the use of an ultra-low (< 10-10 Torr) background vapour pressure. The dependence of the cold collision loss coefficient β on the trapping intensity was measured to permit identification of the different cold collision processes. The largest loss rates observed were those due to hyperfine structure-changing collisions, with a coefficient β = (2±1) x 10-10cm3s-1. A study is presented of a modified magneto-optical trap in which a fraction of the population is shelved into a hyperfine level that does not interact with the trapping light. In this so-called "dark" magneto-optical trap, improved densities of nearly 1012cm-3 have been previously reported for sodium. The application of the technique to caesium is not straightforward due to the larger excited state hyperfine splittings. A simple theory for caesium is presented and its main predictions verified by measurements of density, number and temperature. A density of nearly 1012cm,-3 was indeed obtained but at a temperature substantially higher than in the conventional magneto-optical trap.
 A detailed experimental and theoretical investigation of a magneto-optical trap for caesium atoms is presented. Particular emphasis has been placed on achieving high spatial number densities and low temperatures. Optimizing both of these together enables efficient evaporative cooling from a conservative trap, a procedure which has recently led to the first observations of Bose-Einstein condensation in a dilute atomic vapour. The behaviour of a magneto-optical trap is nominally determined by four independent parameters: the detuning and intensity of the light field, the magnetic field gradient and the number of trapped atoms. A model is presented which incorporates previous treatments into a single description of the trap that encompasses a wide range of its behaviour. This model was tested quantitatively by measuring the temperature of the cloud and its spatial distribution as a function of the four parameters. The maximum density was found to be limited both by the reabsorption of photons scattered within the cloud and by a reduction of the confining force at small light shifts. The nonlinear variation with position of the restoring force was found to be significant in limiting the number of atoms confined to a high density. A maximum density in phase space (defined as the number of atoms in a box with sides of dimension one thermal de Broglie wavelength) of (1.5 ± 0.5) x 10-5 was observed, with a spatial density of 1.5 x 1011 atoms per cm3. Cold collision losses from a caesium magneto-optical trap have been studied with the purpose of assessing their influence on spatial densities. In contrast to previous measurements of similar quantities, these measurements did not require the use of an ultra-low ( A study is presented of a modified magneto-optical trap in which a fraction of the population is shelved into a hyperfine level that does not interact with the trapping light. In this so-called dark magneto-optical trap, improved densities of nearly 1012cm-3 have been previously reported for sodium. The application of the technique to caesium is not straightforward due to the larger excited state hyperfine splittings. A simple theory for caesium is presented and its main predictions verified by measurements of density, number and temperature. A density of nearly 1012cm,-3 was indeed obtained but at a temperature substantially higher than in the conventional magneto-optical trap.
We descrbe a new method for measuring excited-state collisions between optically trapped atoms. With this method, trap-loss collision rates are deduced from the loading behavior of clouds of trapped atoms in the regime where radiation trapping limits the atom density. Our measurements indicate that 85Rb^{85}\mathrm{Rb}85Rb trap-loss collisions occur at significantly smaller rates than expected both from previous work on Cs and from recent models. In addition, the dependence of the trap-loss collisions on the frequency of the light used to excite the atom pairs is also different from that of Cs, suggesting that assumptions about the dynamics in these models need modification.
Collisions between ultra-cold (T << 1K) atoms confined in a magneto- optical trap (MOT) may result in the ejection of atoms from the trap. These collisional loss processes, which involve ground state/excited state collisions, fundamentally limit the density attainable in MOT traps. Although accurate calculations of collision rates between ultra-cold atoms require precise knowledge of the molecular potentials over a long range, the loss rate for Li was recently predicted to be significantly less than for the other alkali metals. Motivated by this result, we are measuring the collisional loss rate of Li in a vapor-cell MOT using a red-detuned laser beam to catalyze the collisions, similar to recent experiments using Rb and Cs. We will report our progress to measure the trap loss rate for {sup 6}Li and {sup 7}Li, which will be compared to investigate an isotopic dependence, as was recently observed for Rb.