Correlations in low dimensional quantum systems

In this thesis I present the work done during my PhD in the area of low dimensional quantum gases. The chapters of this thesis are self contained and represent individual projects which have been peer reviewed and accepted for publication in respected international journals. Various systems are considered, the first of which is a two particle model which possesses an exact analytical solution. I investigate the non-classical correlations that exist between the particles as a function of the tunable properties of the system. In the second work I consider the coherences and out of equilibrium dynamics of a one-dimensional Tonks-Girardeau gas. I show how the coherence of the gas can be inferred from various properties of the reduced state and how this may be observed in experiments. I then present a model which can be used to probe a one-dimensional Fermi gas by performing a measurement on an impurity which interacts with the gas. I show how this system can be used to observe the so-called orthogonality catastrophe using modern interferometry techniques. In the next chapter I present a simple scheme to create superposition states of particles with special emphasis on the NOON state. I explore the effect of inter-particle interactions in the process and then characterise the usefulness of these states for interferometry. Finally I present my contribution to a project on long distance entanglement generation in ion chains. I show how carefully tuning the environment can create decoherence-free subspaces which allows one to create and preserve entanglement.

The optical response of nanostructured surfaces and the composite diffracted evanescent wave model

Investigations of the optical response of subwavelength-structure arrays milled into thin metal films have revealed surprising phenomena, including reports of unexpectedly high transmission of light. Many studies have interpreted the optical coupling to the surface in terms of the resonant excitation of surface plasmon polaritons (SPPs), but other approaches involving composite diffraction of surface evanescent waves (CDEW) have also been proposed. Here we present a series of measurements on very simple one-dimensional subwavelength structures to test the key properties of the surface waves, and compare them to the CDEW and SPP models. We find that the optical response of the silver metal surface proceeds in two steps: a diffractive perturbation in the immediate vicinity (2–3 mu m) of the structure, followed by excitation of a persistent surface wave that propagates over tens of micrometres. The measured wavelength and phase of this persistent wave are significantly shifted from those expected for resonance excitation of a conventional SPP on a pure silver surface.