Ph.D. Thesis - Physics

of O2 to 2 × 10 −12 torr.
Decoherence of the internal states depends on many factors, including fluctuations of
the parameters (amplitude, phase, etc.) that describe the control pulses, fluctuations in
ambient magnetic fields, and processes intrinsic to the atom such as spontaneous emission.
The last of these can result in decoherence even for qubits that have very small spontaneous
emission rates, such as hyperfine qubits, since spontaneous scattering during the Raman
pulses that are used can decohere the states. Although we don’t specifically treat these
decoherence processes in this thesis, we may legitimately hope that internal state coherence
times of several seconds may be obtained, in the event that hyperfine states are used.
7.7 Conclusions and future work
In this chapter we have explored the possibility of using surface-electrode elliptical ion traps
for analog quantum simulation, particularly simulation of quantum spin models. We have
presented calculations of the structure of 2-D and approximately 2-D crystals within such a
trap. These predictions were confirmed experimentally for a small number of ions. We have
also studied, in theory, how micromotion affects the fidelity of a quantum simulation, and
have seen that studies of quantum spin phases are probably possible even in the presence of
micromotion. In addition, magnetic field gradient coils embedded in the ground electrode
of the elliptical trap might prove an excellent way to produce global state-dependent forces
for implementing a variety of spin models.
On the theoretical side, this work is a starting point. For instance, other types of
quantum simulations to which ions may be well-suited have not been considered. It would
be an interesting problem to study the possibility of observing Bose-Hubbard physics in
this system. Furthermore, although we have calculated the effects of micromotion for small
numbers of ions, the work should be extended to larger numbers. Small errors in the pairwise
interactions will propagate across the system as global correlations are created, and it will
be an interesting (but computationally intensive) task to examine how the global fidelity of
the simulation is altered. We note, however, that such errors may be corrected for, provided
adequate controls are available.
Experimentally, a natural first step is attempting to form larger ion crystals in the
elliptical trap. Although the source of the relatively low lifetimes of crystals is unknown,
the heating rates in this system should be measured. If anomalously high heating rates are
a problem, even at 4 K, materials other than copper such as silver or gold, which exhibit
lower heating rates, may be used for trap fabrication. Naturally, we would someday like to
see experimentally if methods based on magnetic field gradients are viable for this purpose,
and whether the effects of micromotion for small ion numbers are as we predict.
In all, the elliptical trap appears to be a much more promising system than arrays of
microtraps for analog quantum simulations with a few tens of ions. The ability to maintain
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