Ph.D. Thesis - Physics

how are single-ion operations to be applied, and what is the effect of the unequal ion-ion
distance in a crystal containing more than two ions?
There exist a number of ways of implementing single-ion operations. The first is simply
to address the ions with a tightly-focused laser. This seems impractical, however, for the
surface-electrode elliptical trap, since the laser would need to be aimed directly toward the
ground electrode. Although it could be applied at an angle, it is unlikely that scatter off this
electrode would not interfere with the states of neighboring ions. A much more appealing
idea would be to do the addressing using rf or microwaves, tuned to the Zeeman or hyperfine
transition being used. The gradient wires used for implementing the state-dependent force
could be turned on to produce a small gradient that can be used for discriminating the
transitions of the individual ions in frequency space. This approach has been successfully
pioneered by our group with laser addressing of ions [WLG + 09], and has been demonstrated
by the Wunderlich group with hyperfine qubits [JBT + 08].
With respect to the unequal ion-ion spacing, we make a few points. The first is that
despite coupling rates that are not perfectly constant across all ion pairs, there is neverthe-
less the possibility of observing interesting physics such as phase transitions. For instance,
the transition from a paramagnetic to an antiferromagnetic state is caused by competition
between a static magnetic field and the ion-ion interaction. A J-coupling rate that varies in
space would add to the uncertainty in measuring the transition point, but this might still be
a useful measurement. The second point is that optical potentials could be used to regulate
the position of ions, as was suggested in Ref. [PC04b]. Furthermore, initial trapping of ions
in an elliptical trap could facilitate loading into a fully optical potential, as discussed in
Ref. [SRM + 08]. In the case of an elliptical trap, additional state-dependent forces may be
added by the magnetic gradient coils, in addition to any forces already present from the
optical potential. Finally, we note that the same level of control required to compensate for
the effects of micromotion could be used to compensate for the unequal ion-ion spacing: if
one can compensate for one effect, then one can compensate for the other.
A final note of caution is that the ultimate number of wires, their geometry, and their
width is limited by the minimum feature size of the fabrication process used. This will in
turn limit the minimum size of the trap and gradient wire structure, limiting the interaction
rates achievable.
7.4 The cryostat and vacuum apparatus
Given the need for reducing heating rates, and the desirability of rapid pumpdown to
UHV pressures, a 4 K closed-cycle cryostat was set up to carry out the trap testing. We
use an Advanced Research Systems (ARS) DE-210 system with a DMX-20 anti-vibration
interface. The system is very similar to the closed-cycle system presented in Ref. [ASA + 09].
The cryostat operates by repeated expansion of high-pressure (250 psi) helium gas into
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