Ph.D. Thesis - Physics

Our experimental results are presented in Fig. 6-9. This composite figure illustrates
several results. First, in (a), it shows that the cloud fluorescence intensity closely matches a
Gaussian fit, allowing measurement of the cloud center to within ±0.5 µm. This translates
into a precision of electric field measurement of about 10 V/m at zero field. The remainder
of this figure shows our measurements of the ˆx and ˆy electric fields as a function of Vtop.
This enables us to determine the required compensation voltages, Vtop = 1.0±0.1 V and
V5 = 1.3±0.3 V. Either V4 or V5 could be used for compensating ˆx. It was convenient to
use V5, since V4 was already used for the secular frequency measurement. The estimated
residual displacement of a single ion at these voltages is 0.2 µm. The nonlinear dependence
of Eˆy on Vtop is due to the anharmonicity of the trap along ˆy, unaccounted for in the above
simple model.
6.3.3 Discussion
Our measurements demonstrate that the compensation voltages for the trap do not agree
well with the prediction of theory. At the theoretical compensation voltages V5 = 0 V
and Vtop = -24.5 V, both Eˆx and Eˆy should be zero. We can determine the stray fields
by measuring the actual values of Eˆx and Eˆy at these settings. At V5 = 0 V and with
Eˆy = 0 (done by setting Vtop to 1 V), Eˆx was measured to be 30 V/m. Unfortunately,
the trap was unstable at the ideal Vtop voltage. Instead of measuring Eˆy at this point, we
extrapolate from Fig. 6-9, subfigure (c), that Eˆy ≈ 2000 V/m. This is in order-of-magnitude
agreement with a parallel plate model, Eˆy = (Vexpt − Videal − V1)/d = 4200 V/m, where
Vexpt is the measured compensation voltage (Vtop = 1.0 V), Videal is the ideal compensation
value (Vtop = -24.5 V), and d is the distance between the top plate and the trap electrodes
(d = 6.3 mm). Of course, these results depend on the agreement between our measured
and predicted secular frequencies. They agree on a 5-10% level, with greater differences
along ˆy, presumably due to the larger stray fields in that direction. These errors increase
the uncertainty in our measurements a bit, but do not change the basic conclusions.
The stray field along ˆx is comparable to those reported for 3-D ion traps [BMB + 98].
However, that along ˆy is on the order of 10 times larger. This suggests significant charging
on either the dielectric on the ion trap, the top plate, or the observation window. This is
clearly a problem when using PCB ion traps. Indeed, these stray fields all but prevented
direct loading at UHV pressures, necessitating the use of the helium buffer gas. This is
mainly because the stray field degrades the trap depth, although it also can cause excessive
rf heating. This is due to the fact that, in the cloud state, driven micromotion couples
to the secular motion. Before compensation, the UHV cloud lifetime was less than 10 s.
Following compensation, ion cloud lifetimes of 10 minutes at 10 −9 torr were observed. This
pressure was limited by residual buffer-gas pressure. As stated above, Rogers 4350B is a
UHV-compatible material after bakeout. Subsequent PCB traps in vacuum have attained
pressures in the 10 −11 torr range.
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