Formation and dynamics of structural defects in ion chains

Non-adiabatic crossing of symmetry breaking phase transitions results in formation of a domain structure and topological defects. The average density of domains depends on the quench rate of the phase transition. Kibble-Zurek mechanism predicts the scaling of the number of domains with quench rate. Phase transitions are ubiquitous in Nature and formation of domains and defects occurs in many different systems. One example of such system is Coulomb crystals of trapped ions, where structural defects can form as a result of symmetry breaking structural transitions between different crystal configurations. In the thesis, we investigate the Kibble-Zurek mechanism using the linear to zigzag structural phase transition in trapped ion Coulomb crystals. First, we analyse the equilibrium properties of crystals in the vicinity of the critical point of the linear to zigzag transition. Next, we show how to derive Kibble-Zurek scaling laws by transforming the equations of motion into a universal form. This mathematical derivation of the scaling laws is generalized for finite and inhomogeneous systems. Two experiments measuring the defect scaling in small trapped ion crystals are described, whose results agree with molecular dynamics simulations. In order to understand and predict defect dynamics we develop the technique for calculating the effective potential in which the defects move. Using this technique we show that heavy molecular ions stabilize the structural defects in zigzag chains and suggest a way of controlling kink motion using the application of electric fields. Finally, conclusions are drawn and possibilities for future work are suggested.Open Acces

Minimally complex ion traps as modules for quantum communication and computing

Optically linked ion traps are promising as components of network-based quantum technologies, including communication systems and modular computers. Experimental results achieved to date indicate that the fidelity of operations within each ion trap module will be far higher than the fidelity of operations involving the links; fortunately internal storage and processing can effectively upgrade the links through the process of purification. Here we perform the most detailed analysis to date on this purification task, using a protocol which is balanced to maximise fidelity while minimising the device complexity and the time cost of the process. Moreover we 'compile down' the quantum circuit to device-level operations including cooling and shutting events. We find that a linear trap with only five ions (two of one species, three of another) can support our protocol while incorporating desirable features such as 'global control', i.e. laser control pulses need only target an entire zone rather than differentiating one ion from its neighbour. To evaluate the capabilities of such a module we consider its use both as a universal communications node for quantum key distribution, and as the basic repeating unit of a quantum computer. For the latter case we evaluate the threshold for fault tolerant quantum computing using the surface code, finding acceptable fidelities for the 'raw' entangling link as low as 83% (or under 75% if an additional ion is available).Comment: 15 pages, 8 figure

Information flow in one-dimensional non-unitary quantum cellular automata

The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time and space, for which an index theory has been proposed for the quantification of the net flow of quantum information across a boundary. While the index is rigid in the sense of begin invariant under finite-depth local circuits, it is not defined when the system is coupled to an environment, i.e. for non-unitary time evolution of open quantum systems. We propose a new measure of information flow for non-unitary QCA denoted the information current which is not rigid, but can be computed locally based on the matrix-product operator representation of the map.Comment: 21 pages, 23 figure