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, 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〉 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. 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 in most magnetic traps. Atoms with an energy
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-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 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.
The finite depth
E of an atom trap results in an upper bound for the energy transfer in collisions with the background gas that will result in heating but not in loss of an atom. The energy transfer rate is accurately predicted as function of the well depth by applying a versatile semiempirical model function for the small-angle differential cross section, covering the full range from pure diffractive scattering to classical scattering. Simple scaling laws for the energy transfer rate are presented that can be readily applied. For the diffraction dominated regime we find an energy transfer rate proportional to
(E/Eref)2 with ${\mathcal{E}}_{\mathrm{ref}}{=(k}_{B}{T}_{b} {\ensuremath{\theta}}_{0}^{2}/4),$ a system-dependent energy determined by the ambient temperature
Tb and the diffraction angle ${\ensuremath{\theta}}_{0}.$ In the classical regime we find the usual result of an energy transfer rate proportional to
(E/Eref)5/6.We present measurements and calculations of the trap loss rate for laser-cooled
87Rb atoms confined in either a magneto-optic trap (MOT) or a magnetic quadrupole trap when exposed to a room-temperature background gas of Ar. We study the loss rate as a function of trap depth and find that copious glancing elastic collisions, which occur in the so-called quantum diffractive regime and impart very little energy to the trapped atoms, result in significant differences in the loss rate for the MOT compared to a pure magnetic trap due solely to the difference in potential depth. This finding highlights the importance of knowing the trap depth when attempting to infer the total collision cross section from measurements of trap loss rates. Moreover, this variation in trap loss rate with trap depth can be used to extract information about the differential cross section.
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
Pt(E) for the collision-induced energy transfer to the trapped ensemble. We describe how to find
Pt(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
87Rb 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.
We confine
85Rb atoms in an optical dipole force trap with a very large detuning from resonance of up to 65 nm. Confinement times of 200 ms, limited only by background-gas collisions, are obtained without additional cooling. A typical trap contains 1300 atoms at a temperature of 0.4 mK and a peak density of 8\ifmmode\times\else\texttimes\fi{}
1011 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. We measure spontaneous photon scatter rates of the trapped atoms to be less than 1.6\ifmmode\times\else\texttimes\fi{}
103 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, corresponding to recoil heating rates below 0.6 mK/s. The far-detuned trap confines atoms with a strong, nearly conservative optical force and negligible atomic excitation.
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.