Spin-guides and spin-splitters: Waveguide analogies in one-dimensional spin chains

Here we show a direct mapping between waveguide theory and spin chain transport, opening an alternative approach to quantum information transport in the solid-state. By applying temporally varying control profiles to a spin chain, we design a virtual waveguide or 'spin-guide' to conduct individual spin excitations along defined space-time trajectories of the chain. We explicitly show that the concepts of confinement, adiabatic bend loss and beamsplitting can be mapped from optical waveguide theory to spin-guides (and hence 'spin-splitters'). Importantly, the spatial scale of applied control pulses is required to be large compared to the inter-spin spacing, and thereby allowing the design of scalable control architectures.Comment: 5 figure

Band Structure, Phase transitions and Semiconductor Analogs in One-Dimensional Solid Light Systems

The conjunction of atom-cavity physics and photonic structures (``solid light'' systems) offers new opportunities in terms of more device functionality and the probing of designed emulators of condensed matter systems. By analogy to the canonical one-electron approximation of solid state physics, we propose a one-polariton approximation to study these systems. Using this approximation we apply Bloch states to the uniformly tuned Jaynes-Cummings-Hubbard model to analytically determine the energy band structure. By analyzing the response of the band structure to local atom-cavity control we explore its application as a quantum simulator and show phase transition features absent in mean field theory. Using this novel approach for solid light systems we extend the analysis to include detuning impurities to show the solid light analogy of the semiconductor. This investigation also shows new features with no semiconductor analog.Comment: 7 page

On the one-dimensional bose gas

The main work of this thesis involves the calculation, using the Bethe ansatz, of two of the signature quantities of the one-dimensional delta-function Bose gas. These are the density matrix and concomitantly its Fourier transform the occupation numbers, and the correlation function and concomitantly its Fourier transform the structure factor. The coefficient of the delta-function is called the coupling constant; these quantities are calculated in the finite-coupling regime, both expansions around zero coupling and infinite coupling are considered. Further to this, the density matrix in the infinite coupling limit, and its first order correction, is recast into Toeplitz determinant form. From this the occupation numbers are calculated up to 36 particles for the ground state and up to 26 particles for the first and second excited states. This data is used to fit the coefficients of an ansatz for the occupation numbers. The correlation function in the infinite coupling limit, and its first order correction, is recast into a form which is easy to calculate for any N, and is determined explicitly in the thermodynamic limit