Ph.D. Thesis - Physics

Figure 6-8: CCD image of a cloud of trapped 88 Sr + ions in San Quentin. The ions are
immersed in 1.0×10 −5 torr helium gas pressure.
at a 1.0×10 −5 torr pressure of ultra-high-purity helium (99.9999% purity). The ion getter
pump was switched off prior to filling. Fig. 6-8 is a CCD image of a cloud of ions trapped
in San Quentin.
6.3.2 Measurement of stray fields
We now turn to the measurement of the stray fields in this trap. This is done by measuring
the change in cloud position as the pseudopotential depth is varied [BMB + 98]. An accurate
value of the stray dc electric field can be calculated from the following model. The electric
field along a coordinate x, at the rf null position, is well approximated by E(x) = E0 +E1x.
For an rf pseudopotential of frequency ω, the ions obey the equation of motion m¨x +
mω 2 x + ecE(x) = 0, which results in a new secular frequency ω1 = (ω 2 + ecE1/m), and
a new cloud center position x0 = ecE0/(mω 2 1 ). By measuring both x0 and ω1, E0 may be
determined.
The measurement is done by translating the 422 nm laser in the ˆx-ˆy plane and fitting
the fluorescence signal, as measured by the photomultiplier tube, to a Gaussian with center
(x0,y0). The trap frequency ωˆn,1 along each direction ˆn is measured by applying a 250 mV
oscillating voltage to the electrode labeled V5. This electrode can stimulate both ˆx and
ˆy motion because electric fields due to voltages on this electrode have components along
both directions. Resonant excitation of the ion motion causes dips in the fluorescence at
ωˆn,1. These measurements are repeated at 10 different rf voltages, and a linear fit of the
cloud center positions x0 and y0 to 1/ω2 ˆx,1 and 1/ω2 ˆy,1 , respectively, gives the stray fields Eˆx0
and Eˆy0. The stray field component along ˆz is not measured or compensated because, in
principle, confinement along this axis is due entirely to dc voltages. Therefore, stray fields
along ˆz do not lead to micromotion. In practice, there are rf field components along ˆz, but
they are much smaller than those along ˆx and ˆy.
139