Ph.D. Thesis - Physics

and is computed, in practice, using numerical modeling. A consequence of this additional
static potential is that ωˆz is different:
ω 2 ˆz
QV
= 8
mΩr2 2
1 −
1
144αmΩ2r3 1U 64QV 2
. (5.4)
z1
To obtain the constants r1, α, and z1, we use the Charged Particle Optics (CPO)
numerical modeling software package to model the trapping potentials. The lattice trap
used for our experiments has a hole diameter of h = 1.14 mm and a spacing between the
centers of the holes of d = 1.64 mm. A square section of the rf electrode measuring 10
lattice sites on each side was used for this modeling; for larger sections than this, the effect
of adding additional sites on the potentials near the center was negligible. From a simulation
of the trap, we obtain the value of the geometric factors: r1 = 3.1±0.1 mm, α = −4.0±1.3,
and z1 = 19 mm for a top plate 15 mm above the rf electrode. Errors arise from the
nonlinear least-squares fit used to obtain r1 and α from the (discrete) simulated potential.
In Fig. 5-3, we compare the numerical potential for the lattice trap to the analytical potential
from the multipole expansion, indicating that near the minimum of a given potential well
the multipole expansion gives an accurate approximation to the simulated pseudopotential.
Note that in this plot the trapping parameters are appropriate for the macroion experiment
(Sec. 5.5), not the 88 Sr + ion experiment (Sec. 5.4).
5.3 Experimental setup for 88 Sr + trapping
In this section, we present the experimental setup for trapping of 88 Sr + ions in a room-
temperature vacuum apparatus. The basic ingredients are:
1. A vacuum chamber containing a mounting place for the ion trap, electrical connections
to it, and a resistive oven for producing a beam of neutral strontium.
2. A pair of lasers to perform Doppler cooling and detection of the trapped ions, another
pair for photoionization, and optics for detection of the ions’ fluorescence signal.
3. Rf electronics for driving the ion trap.
5.3.1 Vacuum chamber and electrical connections
The vacuum chamber used in this work includes a spherical octagon vacuum chamber that
houses the ion trap and electrical feedthroughs, two pumps (ion getter pump and titanium
sublimation pump), and an ionization gauge to monitor pressure. A photograph of the
apparatus is presented in Fig. 5-4, and the components are discussed in detail below.
110