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Physical Review A

Trap-depth determination from residual gas collisions

Janelle Van Dongen, Chenchong Zhu, D. Clement, G. Dufour, James L. Booth, Kirk W. Madison

Published Aug 16, 2011• 27 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.84.022708

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Trap depth determination from background gas collision induced loss rates

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1. D. E. Fagnan, J. Wang, C. Zhu., P. Djuricanin, B.G. Klappauf, J. L Booth, K. W. Madison Phys. Rev. A., 80, 022712 (2009) 2. D. Hoffmann, S. Bali, T. Walker, Phys. Rev. A. 54, R1030 (1996) 3. S. Bali, D. Hoffmann, T. Walker, Europhys. Lett, 27 (4), pp.273-277 (1994) • We have demonstrated a technique for determining the trap depth for any type of trap using loss rates arising from collisions with background gas particles.

Bulletin of the American Physical Society•May 27, 2010•0 citations
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.
The authors demonstrate a new method for measuring the C6{}_{6}6​ van der Waals coefficient of the Rb-Rb interaction potential from the loss rate of atoms confined in a shallow atom trap of tunable depth. The technique is based on the universal nature of the room-temperature collisions, which depends only on the long-range potential between the collision partners.
This thesis describes an investigation and application of the loss of laser cooled atoms from a trap induced by background collisions. The loss rate constant depends on the density of background gas and the velocity averaged collisional loss cross section due to collisions. The velocity averaged collisional loss cross section can be calculated and its dependence on trap depth was verified using a magneto-optical trap. This verification involved measurements of the loss rate constant for a quadrupole magnetic and a magneto-optical trap and measurement of the density of Ar background gas using a residual gas analyzer. The second part of the thesis focuses on an application of these measurements of the loss rate constant to measure the pressure of the background gas. The experimental progress to date on the atom pressure sensor is provided.
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.
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){P}_{t}(E)Pt​(E) for the collision-induced energy transfer to the trapped ensemble. We describe how to find Pt(E){P}_{t}(E)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^{87}\mathrm{Rb}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 present measurements and calculations of the trap loss rate for laser-cooled 87Rb^{87}\text{R}\text{b}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.