Ph.D. Thesis - Physics

Chapter 7
Quantum simulation in
surface-electrode elliptical ion
traps
As discussed at length in this thesis, two-dimensional arrays of trapped ions have great
potential for a number of types of quantum simulations, most particularly for the simulation
of spin frustration. We report in Ch. 5 that an array of individual microtraps, although
appealing for its ability to generate an evenly-spaced array of ions, suffers major drawbacks
in the interaction rate between neighboring trapped ions, whether considering motional
coupling or the simulated spin-spin interaction rate. This motivates our present study of
ion-ion interactions between ions in the same potential well that form a 2-D array through
mutual Coulomb repulsion. In this case, the motional coupling rate is on the same order of
magnitude as that in a linear ion trap with the same ion-ion spacing.
In this chapter, we explore one example of an trap that creates a 2-D array of ions: a
surface-electrode elliptical Paul trap. We choose the Paul trap approach in order to avoid the
large Zeeman shifts and crystal rotation associated with Penning traps, as we did in Ch. 5.
The surface-electrode geometry, as in Ch. 6, is beneficial for simplicity of microfabrication
and eventual scaling down to microscopic sizes, if required. Prior to this work, the only
2-D ion crystal prepared in a Paul trap had been in a linear trap. An added benefit of
our elliptical trap approach is the ability, in principle, to apply magnetic field gradients
to wires that reside in the plane of the trap electrodes, creating magnetic field gradients
that can effect state-dependent forces in a manner similar to that proposed in Ref. [CW08],
but with theoretically much stronger interaction rates. This is another advantage of the
surface-electrode elliptical trap over other methods for generating a 2-D array of ions in the
same potential well.
A sensible objection to this technique is the existence of micromotion that cannot be
compensated away and that affects every ion in the trap. The reason for this is that
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