Ph.D. Thesis - Physics

macroscopic ions across lattice sites. In Sec. 5.6, we evaluate the trap design by computing
the interaction rates as a function of trap scale in lattice traps. In Sec. 5.7, we conclude on
this work.
5.1 Proposals for quantum simulation in lattice ion traps
Quantum information theorists have put forward several proposals for quantum operations
in 2-D arrays of trapped ions. A 2000 paper from Cirac and Zoller suggests using ions in
an array of microtraps to form the basis of a scalable quantum computer, in which an ion
is moved from site to site within the array to interact with ions contained therein [CZ00].
Later, as we discussed in Ch. 4, the spin model proposal of Porras and Cirac suggested
that an array of microtraps could be used to implement quantum simulations of interesting
physics such as spin frustration [PC04b].
A subsequent proposal from Chiaverini and Lybarger [CW08] suggested using an array of
microtraps to implement a 2-D quantum simulation. In their scheme, microcoils surrounding
each lattice site address individual ions contained therein with microwave radiation, effecting
single-qubit rotations. In addition, magnetic field gradients may be applied which serve the
same purpose as the lasers in the Porras-Cirac scheme, generating state-dependent forces
that translate into effective spin-spin interactions.
The commonality between the two is the requirement of a 2-D array of trapped ions. The
advantages of a 2-D array of microtraps are that the position of each ion is well-determined
by the trap electrodes, and that, conceivably, dc compensation electrodes could be provided
for each site. This is in contrast to a trap in which all ions are contained in the same
potential well. In such a trap, the ion-ion distance can vary, especially near the edge of the
crystal, and micromotion may pose a problem. However, in this chapter, we focus on arrays
of Paul traps, or lattice ion traps.
5.2 Lattice trap design and theory
The model we study in this chapter is a layered planar rf electrode geometry that creates a
2-D ion lattice. The ion trap consists of a planar electrode with a regular array of holes, held
at a radiofrequency (rf) potential, mounted above a grounded planar electrode. A single ion
is trapped above each hole in the rf electrode (Fig. 5-1). Ions will be preferentially loaded
above the trap electrode at the intersection of the Doppler cooling and photoionization
beams, allowing the user to write an arbitrary 2-D lattice structure. We view this design
as an archetype of 2-D Paul trap arrays, in the sense that conclusions drawn about some
properties of this trap may translate to other, similar, trap designs.
Our lattice trap is an extension of the three-dimensional ring Paul trap [Gho95]. Follow-
ing this reference, we first review the theory of the ring trap. The ring electrode geometry
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