Ph.D. Thesis - Physics

Electronics
The electronics for this experiment were similar to those used in previous ones (Chs. 5 and
6). Briefly, dc voltages were supplied to four of the dc electrodes on the trap using an
eight-channel voltage source that interfaces to the computer. The dc signals were filtered
by standard R-C low-pass filters with a cutoff frequency of about 100 kHz. This was chosen
to provide an rf short to ground for the dc electrodes at the drive frequency (3.5 MHz)
while still allowing the lower-frequency voltages used for secular frequency measurement to
pass through.
An rf signal was produced by an Agilent 33250 function generator and sent directly
to the helical resonator. To produce the proper voltages, no additional rf amplifier was
required. The resonator was mounted to the table and connected to the chamber with an
rf feedthrough. Grounding straps connected the rf input with the function generator, the
cryostat hoses, and earth ground, and also provided the rf ground for the dc filters.
7.5.2 Secular frequency measurements
Secular frequencies were measured by using a low-amplitude voltage applied to the electrode
DC2. The amplitude required varied a great deal between the different motional frequencies.
Prior to this, basic compensation of the trap was done by setting the dc voltages such
that the ion cloud did not move when the rf amplitude was changed. There was actually a
significant movement of the ion cloud (tens of microns) with a change in Vc of only 0.1 V;
therefore, the vertical direction could be roughly compensated by setting Vc such that the
cloud did not move out of the laser when the rf was changed. The final set of dc voltages
were V1 = -3.90 V, V2 = 1.56 V, V3 = V4 = 0 V, and Vc = -2.62 V. Fig. 7-22 is a plot of one
data set taken at a sequence of RF voltages with these dc voltages. The secular frequencies
were measured by exciting the ions at their motional frequencies and observing drops in
their fluorescence, as discussed in Sec. 5.4.
The CPO-computed frequencies for this voltage set are plotted below, in Fig. 7-23. One
sees that the agreement is not very good. Why is this? For one thing, note that the
theoretical frequencies have changed a great deal from those with only rf confinement (cf.
Fig. 7-3). Therefore, the dc voltages do not merely move the position of the ions; they
change the curvature of the trap itself. A portion of the dc voltages here merely nulls stray
fields that existed in the first place. Some portion, however, also contributes to altering the
trap curvature. Another clue is provided by the fact that although ωˆx + ωˆy = ωˆz to fairly
good agreement in the simulation, this relation does not hold for the experimental data,
indicating that dc voltages have a contributing effect.
Another possible source of error is that the rf voltage measured on the exterior of
the cryostat does not necessarily equal the voltage on the trap. The degree to which it
does depends greatly on the specific experimental setup. The wire extending from the
feedthrough is quite long in order to reach the 4 K area and be properly heat-sunk on the
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