Ph.D. Thesis - Physics

principal method of measuring the trap potentials is by measuring the secular frequencies,
as was done with both macroions and 88 Sr + ions. The repulsion experiment using macroions
is primarily useful for demonstrating the possibility of measuring properties of a trap such
as the electrostatic screening factor using a simpler experimental setup than that needed
for atomic ions.
Building a prototype trap of a macroscopic scale (mm rather than 10’s of µm) is useful
because it enables us to very closely examine a given design in less difficult experimental
circumstances, for instance without excessive heating due to small ion-electrode distances or
laser scatter off the trap. In this case, our investigation of the interaction strength between
the macroions led somewhat indirectly to our conclusions about the poor scaling properties
of lattice traps from Sec. 5.6.
The poor scaling behavior of lattice traps indicates that other avenues should be sought
for creating 2-D lattices of trapped ions. Some possibilities include confining ions within the
same trap region in Paul traps, or development of a way to apply global state-dependent
forces to ions in Penning traps despite the rapid rotation of the ion crystal. Another
possibility would be to modify the electrode design of a lattice trap in such a way that
the ratio of trap depth to motional frequency is optimized; perhaps then sufficient coupling
rates could be achieved. It remains to be seen which method of preparing 2-D lattices of
ions, if any, will succeed in supporting analog quantum simulation.
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