Ph.D. Thesis - Physics

Chapter 5
Lattice ion traps for quantum
simulation
In this chapter we turn to a theoretical and experimental investigation of lattice ion traps
for quantum simulation. Many schemes for doing quantum simulation and computation,
such as the one presented in Ch. 4, rely on a regular array of trapped ions; a lattice-style
architecture, in which single ions are arranged in a regular array of microtraps, is one way
of achieving this. If the spatial extent of the array lies in more than one dimension, then
interesting physics such as spin frustration becomes accessible, as we noted in the last
chapter.
This chapter describes the first implementation of such a trap. We first present a theo-
retical model describing one method of generating an array of Paul traps. Our experimental
work is driven by the question of whether the trap potentials match the predictions of our
model, as well as the question of whether interactions between ions in neighboring wells
are observable. For these measurements, we trap both both 88 Sr + ions and charged micro-
spheres. Having obtained an answer, we move to the theoretical question of the interaction
rates in such a trap. We wish to calculate, based on observations of the trap, how both
the motional coupling rate and simulated spin-spin interaction scale with the overall size of
the trap. With this calculation done, one may evaluate the utility of this trap design for
our ultimate goal: analog quantum simulation of spin frustration. The main results of this
work were published as Ref. [CLBC09].
The chapter is organized as follows. In Sec. 5.1, we briefly summarize some theoretical
proposals for using lattice ion traps for analog quantum simulation, focusing on physics
that can be studied with a 2-D but not with a 1-D array of ions. In Sec. 5.2, we present our
theoretical model of the lattice ion trap. In Sec. 5.3, we discuss the experimental setup for
trapping atomic ions, including the lasers, vacuum system, and the trap itself. In Sec. 5.4,
we report on our results of trapping both ion clouds and single ions, and measuring their
motional frequencies. In Sec. 5.5, we report on the measurement of interactions between
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