Measuring the temperature of the 87 Rb ensemble in the MOT

indicated by the dashed line in (a), and a fitted Gaussian distribution (red line).

radius was extracted from these fits. An example of a MOT fluorescence image, along with a Gaussian fitted cut through the horizontal center line of the cloud is presented in Fig. 2.12. During the experiments, vertical and horizontal cuts were taken to ensure the isotropic nature of the distribution.

2.3.5

Measuring the temperature of the

Rb ensemble in the

MOT

The velocity distribution of atoms in the MOT is quasi-thermal, and can be closely approximated by a 1D-Maxwell-Boltzmann distribution in each direction [2]. In this case the temperature can be defined through the width of the velocity distribution, which is centered around zero, i.e. in one dimension 1

2kBT = 1 2mv

2 _{where v is the RMS}

velocity of the distribution.

The temperature of the atoms in the MOT was measured following the techniques of ref. [95]. The technique was roughly based on the method of Ref. [96], which assumes that if the trap is suddenly switched off, the atoms that were held in the trap will expand ballistically at a rate that is characteristic of their initial temperature. The expansion follows

ω2(t) = ω2(0) + kBT

m

!

t2 (2.6)

where ω is the 1/e radius of the atom cloud. Reference [95] showed that instead of turning off the trap completely, it is sufficient to turn off only one dimension (i.e. just one pair of counter-propagating laser beams of the MOT), and to observe the ballistic expansion in this dimension. This makes the observation of expansion easier by virtue of the atoms being constantly illuminated by the four beams beams which remain on. If the x axis is defined as the propagation axis of the beam which is switched off, then

0 1 2 0.0 0.2 0.4 0.6 0.8 1.0 toff(ms) 2 (10 -7 m 2 ) x t (ms) 0 0.5 1 2.5 3 off (c) (d)

Figure 2.13: (a) A picture of a hard disk of a computer showing needle and voice coil (b) A picture of the fast shutter (made from the hard disk voice coil in (a)) on the experiment. This shutter is used in the temperature measurement of the atoms in the MOT. (c) A Graph of the square of the atom cloud 1/e radius in the x direction ωx

against time after the shutter blocks the x direction MOT beams. The line is a fit to equation 2.7. The temperature of the atom cloud in this measurement was found to be 127 ±10 µK. Each data point is an average of three consecutive measurements. (d) A sequence of fluorescence images of a cloud of atoms in the MOT at varying times t after the x direction MOT beams are blocked, showing the ballistic expansion of the cloud in this dimension.

in one dimension equation 2.6 becomes

ω_x2(t) = ω_x2(0) + kBT

m

!

t2 (2.7)

Since the line of sight of the CCD camera is aligned 45◦ to the x axis, the observed 1/e radius of the cloud on expansion ωr is related to the 1/e radius of the cloud in the

expansion direction ωx by

ω2_r(t) = (ω2_x(t) + ω_y2(t))/2 (2.8) where ωy is the 1/e radius of the cloud in the y direction. (Note, x and y define the

horizontal plane which does not include the magnetic coils, with z being the remaining orthogonal vertical axis.) There was negligible expansion of the cloud in the y and z directions during the 1D expansion, and hence observation of the atoms in the plane of the CCD chip is sufficient to calculate the temperature of the atoms.

This 1D release and recapture method relies on the fast on/off switching of one of the pairs of laser beams of the MOT. This was achieved by building an optical chopper from the voice-coil actuator of a hard disk drive [97]. The switch time from "beam on" to "beam off" achieved by this shutter was 150 − 200 µs depending on the drive current used, and the "beam off" time could be varied from 400 µs up to 10 ms. A picture of the shutter (b) and the corresponding hard drive (a) is presented in Fig. 2.13. The shutter was synchronized with the CCD camera using two transistor-transistor-logic (TTL) pulses originating from a DAC card connected to a PC running a control program written in Labview. The CCD exposure time was set to 0.6 ms (the minimum allowed value). Fluorescence images were recorded for different "beam off" holding times toff. A

series of such images is presented in Fig. 2.13 (d). From fitting cuts of the expansion images to Gaussian distributions, ωr and hence via equation 2.8 ωx were determined. ω2_x is plotted against expansion time toff in Fig. 2.13 (c). The red line is a best fit to

equation 2.7, and yields a temperature of the atoms of 127 ± 10µK.

2.3.6

Chopping of the MOT

Of the ensemble of87Rb atoms in a MOT, a certain proportion (typically around 10%) are in the excited 52_P

3/2 level due to laser excitation. The ionization continuum of Rb

lies 2.59 eV above this level, and so absorption of a photon with a wavelength below 478 nm results in ionization of Rb. Any Rb+ generated in this way is then loaded into the ion trap. The successful analysis of ion-neutral reactions requires that any ions present in the ion trap are produced from chemical reactions, and not from other sources. Also, the photoionisation can be so efficient that vast amounts of Rb+ ions are loaded quickly, and hence distorting and even melting the original ion crystal of interest (see section 2.2.4). It is therefore imperative that no Rb+ _{are produced by photoinisation.}

To ensure this, the ion cooling lasers (at 397 nm for Ca+ and 493 nm for Ba+) and the Rb cooling laser (at 780 nm) were alternatively chopped by a mechanical chopper at 1 kHz (see Fig. 2.14 (c)) such that when Rb was being cooled, and hence had some

0 2000 4000 6000 8000 10000 12000 14000 B 0 200 400 600 800 1000 0 2000 4000 6000 8000 10000 12000 14000 B A (a) (b) (c)

Figure 2.14: (a) Fluorescence image of an unchopped MOT with an intensity plot of a cut through the center row (black dots) and a Gaussian fit (red line) (b) Same as (a) but for optical chopping of all of the MOT beams at 1000 Hz. (c) A picture of the chopping wheel showing fiber out-coupling of the 780 nm (blue fiber) and 397 nm (yellow fiber) beams that are alternately chopped.

population in 5 2_P

3/2, no intense source of direct (397 nm) or near-direct (493 nm)

ionizing photons was present. There was a period of ≈ 50 µs after each on or off cycle where all laser sources are blocked, which was sufficient time for the decay of excited state atoms (excited state lifetime τ = 26 ns for87_{Rb), or ions (τ = 7 ns for Ca}+_{) back}

to the ground state. Note that the repumping lasers (866 nm for Ca+ _{and 650 nm for}

Ba+_{) remained constantly on in experiments to avoid trapping in the long lived} 2_D 3/2

states during chopping of the cooling lasers.

When the MOT laser beams were turned off, the atom cloud expanded ballistically in three dimensions, similar to the 1D case as seen in the temperature measurements in section 2.3.5. Once the beams were turned on again, the atoms were forced back towards the trap center. In the 1 kHz optical chopping used in the experiments of this work, the atoms expanded and contracted with a period of 1 ms. The time averaged result was that the atom cloud reduced in atom number, and its width increased, re- sulting in reduced atom number densities. A comparison is made in Fig. 2.14 between a MOT without (a) and with (b) optical chopping at 1 kHz. Next to each false color fluorescence image is a cut through the center of the cloud with a fit to a Gaussian distribution. The 1/e radius of the fitted Gaussian for the chopped MOT was approx- imately double that of the corresponding unchopped MOT, which in itself implies a reduction of number density by a factor of 8. The number of atoms also reduces due to the loss of atoms on ballistic expansion, resulting in a typical total reduction in density during chopping of a factor of 50, i.e. from ∼ 5 × 1010 cm−3 to ∼ 1 × 109 cm−3. Note that the values stated were typical but that under the right conditions, density differences of up to a factor of 200 were possible.

It is interesting to note that this reduction in density upon chopping turned out to be useful for the study of fast reaction processes, since at lower densities, the reaction rate was slower, and hence easier to observe. These low densities also minimized the influence of three-body reactive processes, allowing direct study of the two body processes that were the focus of this work.