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.

“Step by step”: high frequency short-distance epizoochorous dispersal of aquatic macrophytes

Aquatic macrophytes can successfully colonise and re-colonise areas separated by space and time. The mechanisms underlying such “mobility” are not well understood, but it has often been hypothesised that epizoochory (external dispersal) plays an important role. Yet, there is only limited, and mostly anecdotal, evidence concerning successful epizoochorous dispersal of aquatic macrophytes, particularly in the case of short-distance dispersal. Here we examine in situ and ex situ dispersal of aquatic macrophytes, including three invasive alien species. A high frequency of Lemna minor Linnaeus dispersal was observed in situ, and this was linked to bird-mediated epizoochory. We concluded that wind had no effect on dispersal. Similarly, in an ex situ examination Lemna minuta Kunth and Azolla filiculoides Lamarck, were found to be dispersed with a high frequency by mallard ducks (Anas platyrhynchos). No dispersal was measured for Elodea nuttalli (Planchon) H. St. John. It is concluded that short-distance or “stepping-stone” dispersal via bird-mediated epizoochory can occur with high frequencies, and therefore can play an important role in facilitating colonisation, range expansion and biological invasion of macrophytes.