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arXiv:2310.04583 · Physical Review A

Trapped-particle evolution driven by residual gas collisions

Avinash Deshmukh, Riley A. Stewart, Pinrui Shen, James L. Booth, Kirk W. Madison

Published Mar 22, 2024• 5 citations
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Abstract

We present a comprehensive mathematical model and experimental measurements for the evolution of a trapped-particle ensemble driven by collisions with a room-temperature background vapor. The model accommodates any trap geometry, confining potential, initial trapped distribution, and other experimental details; it only depends on the probability distribution function ${P}_{t}(E)$ for the collision-induced energy transfer to the trapped ensemble. We describe how to find ${P}_{t}(E)$ using quantum scattering calculations and how it can be approximated using quantum diffractive universality. We then compare our model to experimental measurements of a $^{87}\mathrm{Rb}$ ensemble energy evolution exposed to a room-temperature background gas of Ar by means of a single parameter fit for the total collision rate $\mathrm{\ensuremath{\Gamma}}$. We extracted a collision rate of $\mathrm{\ensuremath{\Gamma}}=0.649(2)\phantom{\rule{4pt}{0ex}}{\text{s}}^{\ensuremath{-}1}$. We further refine our analysis by using monotonic Gaussian process regression to smooth the experimental data, which extracts a collision rate of $\mathrm{\ensuremath{\Gamma}}=0.646(1)\phantom{\rule{4pt}{0ex}}{\text{s}}^{\ensuremath{-}1}$. This is compared to a value of 0.67(1) ${\text{s}}^{\ensuremath{-}1}$ found by the commonly used method of zero-trap depth extrapolation, a 3.5% correction that is a result of our model fully taking ensemble loss and heating into account. Finally, we report a fivefold increase in the precision of our collision rate extraction from the experimental data and a tenfold increase in the precision of our collision rate extraction from the smoothed experimental data.

DOI
10.1103/physreva.109.032818

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We present a method for determining the depth of an atomic or molecular trap of any type. This method relies on a measurement of the trap loss rate induced by collisions with background gas particles. Given a fixed gas composition, the loss rate uniquely determines the trap depth. Because of the ``soft'' long-range nature of the van der Waals interaction, these collisions transfer kinetic energy to trapped particles across a broad range of energy scales, from room temperature to the microkelvin energy scale. The resulting loss rate therefore exhibits a significant variation over an enormous range of trap depths, making this technique a powerful diagnostic with a large dynamic range. We present trap depth measurements of a Rb magneto-optical trap using this method and a different technique that relies on measurements of loss rates during optical excitation of colliding atoms to a repulsive molecular state. The main advantage of the method presented here is its large dynamic range and applicability to traps of any type requiring only knowledge of the background gas density and the interaction potential between the trapped and background gas particles.
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Grazing collisions with background gas are the major cause of trap loss and trap heating in atom traps. To first order, these effects do not depend on the trap density. In collisionally opaque trapped atom clouds, however, scattered atoms with an energy E larger than the effective trap depth Eeff,{\mathcal{E}}_{\mathrm{eff}},Eeff​, which are destined to escape from the atom cloud, will have a finite probability for a secondary collision. This results in a contribution to the heating rate that depends on the column density 〈nl〉〈\mathrm{nl}〉〈nl〉 of the trapped atoms, i.e., the product of density and characteristic size of the trap. For alkali-metal atom traps, secondary collisions are quite important due to the strong long-range interaction with like atoms. We derive a simple analytical expression for the secondary heating rate, showing a dependency proportional to 〈nl〉Eeff1/2.〈\mathrm{nl}〉 {\mathcal{E}}_{\mathrm{eff}}^{1/2}.〈nl〉Eeff1/2​. When extrapolating to a vanishing column density, only primary collisions with the background gas will contribute to the heating rate. This contribution is rather small, due to the weak long-range interaction of the usual background gas species in an ultrahigh-vacuum system---He, Ne, or Ar---with the trapped alkali-metal atoms. We conclude that the transition between trap-loss collisions and heating collisions is determined by a cutoff energy $200 \ensuremath{\mu}\mathrm{K}<~{\mathcal{E}}_{\mathrm{eff}}<~400 \ensuremath{\mu}\mathrm{K},$ much smaller than the actual trap depth E\mathcal{E}E in most magnetic traps. Atoms with an energy Eeff<E<E{\mathcal{E}}_{\mathrm{eff}}<E<\mathcal{E}Eeff​<E<E escape into the Oort cloud: a mechanism of effective traploss in the microkelvin range of trap temperatures. We present results of secondary heating rates for the alkali-metal atoms Li through Cs as a function of the effective trap depth, the column density of the trap, and the species in the background gas. The predictions of our model are in good agreement with the experimental data of Myatt for heating rates in high-density 87Rb{}^{87}\mathrm{Rb}87Rb-atom magnetic traps at JILA, including the effect of the rf shield and the composition of the background gas. It is shown that collisions with atoms from the Oort cloud also contribute to the heating rate. For 85Rb{}^{85}\mathrm{Rb}85Rb the calculated heating rate is below the experimentally observed value at JILA, supporting the idea that inelastic collisions in the trap are the major source of heating.
We derive a simple formula for the heating rate that arises from quantum-diffractive background gas collisions in atom traps. This result appears to explain the residual heating rates reported for recent experiments with a Cs vapor-loaded, far-detuned optical trap at $\ensuremath{\simeq}{10}^{\ensuremath{-}9}$ Torr [Phys. Rev. Lett. 81, 5768 (1998)]. Diffractive collisions may determine the minimum heating rates achievable in shallow all-optical or magnetic atom traps operating at low temperature and high density.
Heating in a magnetic trap was observed through measurements of heated fraction. These results are in agreement with a trap simulation, which can also be used to predict per-atom heating rate . The heating rate for an ensemble with non-zero temperature is significantly smaller than the heating rate for an ensemble with zero temperature. Future work includes refining FH’ measurements, investigating possible deviations of the data from the simulation at large trap depths, and characterizing heating between trapped Rb and other gases, such as 40Ar. dt dE /