Ph.D. Thesis - Physics

Along ˆy, the spacing is dˆy = 28±3 µm, while along ˆx it is dˆx = 17±3 µm. These values are
consistent with the theoretical values of dˆy = 29.6 µm and dˆx = 17.1µm.
Again, it was not possible to crystallize larger numbers of ions, and therefore confir-
mation of the crystal structure for higher numbers of ions was not done. However, we do
now have some confidence that the crystal structure in elliptical traps may be accurately
computed. There are a number of possible reasons for the low ion number. Among them
are the stability of the lasers used, the fact that crystals were only observed at relatively low
trap depths (0.3 eV), and the possibility of heating from the rf electrode rendering larger
crystals unstable. Indeed, the lifetime of a single ion in the absence of cooling light was at
most a few seconds, indicating that heating may indeed be a problem.
7.6 Discussion: connection to quantum simulation
We have now presented the design and testing of a new method for preparing a 2-D Coulomb
crystal in a Paul trap: the surface-electrode elliptical trap. The next step is to evaluate the
usefulness of this trap for quantum simulation, focusing again on the challenging problem
of spin frustration. We frame this discussion in terms of the requirements posed in Sec. 4.3.
There, we note that a viable trap design must:
1. Provide a regular array of stationary qubits in at least two spatial dimensions.
2. Enable sufficient control over each qubit to implement the desired simulation.
3. Possess, in principle, a low enough decoherence rate to perform meaningful simulations
given certain coupling rates.
We address these criteria one-by-one.
7.6.1 Regular array of stationary qubits
We have calculated crystal structures for the elliptical trap presented in this chapter, but
it is seen from these that a truly regular array of ions is not produced. The reason for this
is that the test trap was designed with more difference between the radial frequencies ωˆx
and ωˆy than is strictly necessary to support a 2-D crystal with fixed ion positions.
Recent calculations [BKGH08, BH09] have suggested that in a 2-D ion crystal regular
lattice structures near the center of the lattice may be observed. We expect that, in our trap,
as ωˆx → ωˆy, that such regular structures will also appear. The calculations of Sec. 7.1.2
support this hypothesis.
7.6.2 Sufficient controls
We have outlined in this chapter two methods for implementing the state-dependent forces
required for quantum simulation of spin models: optical forces and magnetic field gradients.
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