Formation and dynamics of structural defects in ion chains
File(s)
Author(s)
Nigmatullin, Ramil
Type
Thesis
Abstract
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.
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.
Version
Open Access
Date Issued
2014-03
Date Awarded
2014-12
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Plenio, Martin
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)