Ions trapped in Paul traps provide a system which has been shown to exhibit most of the properties required to implement quantum information processing. In particular, a two-dimensional array of ions has been shown to be a candidate for the implementation of quantum simulations. Microfabricated surface geometries provide a widely used technology with which to create structures capable of trapping the required two-dimensional array of ions. To provide a system which can utilise the properties of trapped ions a greater understanding of the surface geometries which can trap ions in two-dimensional arrays would be advantageous, and allow quantum simulators to be fabricated and tested. In this thesis I will present the design, set-up and implementation of an experimental apparatus which can be used to trap ions in a variety of different traps. Particular focus will be put on the ability to apply radio-frequency voltages to these traps via helical resonators with high quality factors. A detailed design guide will be presented for the construction and operation of such a device at a desired resonant frequency whilst maximising the quality factor for a set of experimental constraints. Devices of this nature will provide greater filtering of noise on the rf voltages used to create the electric field which traps the ions which could lead to reduced heating in trapped ions. The ability to apply higher voltages with these devices could also provide deeper traps, longer ion lifetimes and more efficient cooling of trapped ions. In order to efficiently cool trapped ions certain transitions must be known to a required accuracy. In this thesis the 2S1/2 → 2P1/2 Doppler cooling and 2D3/2 → 2D[3/2]1/2 repumping transition wavelengths are presented with a greater accuracy then previous work. These transitions are given for the 170, 171, 172, 174 and 176 isotopes of Yb+. Two-dimensional arrays of ions trapped above a microfabricated surface geometry provide a technology which could enable quantum simulations to be performed allowing solutions to problems currently unobtainable with classical simulation. However, the spin-spin interactions used in the simulations between neighbouring ions are required to occur on a faster time-scale than any decoherence in the system. The time-scales of both the ion-ion interactions and decoherence are determined by the properties of the electric field formed by the surface geometry. This thesis will show how geometry variables can be used to optimise the ratio between the decoherence time and the interaction time whilst simultaneously maximising the homogeneity of the array properties. In particular, it will be shown how the edges of the geometry can be varied to provide the maximum homogeneity in the array and how the radii and separation of polygons comprising the surface geometry vary as a function of array size for optimised arrays. Estimates of the power dissipation in these geometries will be given based on a simple microfabrication.
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