Ph.D. Thesis - Physics

Chapter 8
Motivation for and theory of
ion-ion coupling over a wire
In the first two parts of the thesis, we explored digital and analog quantum simulation
using two different quantum technologies: nuclear magnetic resonance and trapped ions.
We also saw that both NMR and the types of ion traps studied in Part II have only a
limited scalability, up to at most perhaps tens of interacting particles. This provides the
motivation for studying a way to scale up quantum simulation to truly arbitrary numbers
of interacting particles.
We now turn to the third and final part of the thesis. The main goal of the research
presented here is the coupling of two trapped ions over a conducting wire. This little-studied
system could potentially be used to scale up ion trap quantum simulation, linking ions in
separate trap regions through the image charges induced in the wire by the motion of the
ions. Application to both digital and analog quantum simulation is conceivable, and in
contrast to the trap designs of Chs. 5 and 7, such coupling is, in principle, electronically
switchable, and there is no apparent limit to the number of ions that may be networked in
this way.
In this chapter, we present a theoretical treatment of the coupling of two ions over a
wire. We explain that the system has the form of two coupled oscillators, with the coupling
mediated by the image charges in the wire rather than by free-space Coulomb coupling,
which is the most common case with ion trap quantum simulation. We also present a
calculation of this coupling rate, showing how it depends on the experimental parameters
such as the ion-wire distance, the trap frequencies, and the capacitance of the wire. This
calculation permits us to set bounds on these parameters for an experimental demonstration
of the coupling, and also to estimate the rates of certain decoherence processes in the system.
These results are included in Ref. [DLC + 09b].
The chapter is organized as follows. In Sec. 8.1, we motivate the study of ion-ion
coupling over a wire. In Sec. 8.2, we present the theory of ion-ion coupling over a wire
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