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.

Computational studies of the transverse structure of AGN jets

Both the emission properties and the evolution of the radio jets of Active Galactic Nuclei are dependent on the magnetic (B) fields that thread them. A number of observations of AGN jets suggest that the B fields they carry have a significant helical component, at least on parsec scales. This thesis uses a model, first proposed by Laing and then developed by Papageorgiou, to explore how well the observed properties of AGN jets can be reproduced by assuming a helical B field with three parameters; pitch angle, viewing angle and degree of entanglement. This model has been applied to multifrequency Very Long Baseline Interferometry (VLBI) observations of the AGN jets of Markarian 501 and M87, making it possible to derive values for the helical pitch angle, the viewing angle and the degree of entanglement for these jets. Faraday rotation measurements are another important tool for investigating the B fields of AGN jets. A helical B field component should result in a systematic gradient in the observed Faraday rotation across the jet. Real observed radio images have finite resolution; typical beam sizes for cm-wavelength VLBI observations are often comparable to or larger than the intrinsic jet widths, raising questions about how well resolved a jet must be in the transverse direction in order to reliably detect transverse Faraday-rotation structure. This thesis presents results of Monte Carlo simulations of Faraday rotation images designed to directly investigate this question, together with a detailed investigation into the probabilities of observing spurious Faraday Rotation gradients as a result of random noise and finite resolution. These simulations clearly demonstrate the possibility of detecting transverse Faraday-rotation structures even when the intrinsic jet widths are appreciably smaller than the beam width.

The development of new methods for high resolution radio astronomy imaging

Very Long Baseline Interferometry (VLBI) polarisation observations of the relativistic jets from Active Galactic Nuclei (AGN) allow the magnetic field environment around the jet to be probed. In particular, multi-wavelength observations of AGN jets allow the creation of Faraday rotation measure maps which can be used to gain an insight into the magnetic field component of the jet along the line of sight. Recent polarisation and Faraday rotation measure maps of many AGN show possible evidence for the presence of helical magnetic fields. The detection of such evidence is highly dependent both on the resolution of the images and the quality of the error analysis and statistics used in the detection. This thesis focuses on the development of new methods for high resolution radio astronomy imaging in both of these areas. An implementation of the Maximum Entropy Method (MEM) suitable for multi-wavelength VLBI polarisation observations is presented and the advantage in resolution it possesses over the CLEAN algorithm is discussed and demonstrated using Monte Carlo simulations. This new polarisation MEM code has been applied to multi-wavelength imaging of the Active Galactic Nuclei 0716+714, Mrk 501 and 1633+382, in each case providing improved polarisation imaging compared to the case of deconvolution using the standard CLEAN algorithm. The first MEM-based fractional polarisation and Faraday-rotation VLBI images are presented, using these sources as examples. Recent detections of gradients in Faraday rotation measure are presented, including an observation of a reversal in the direction of a gradient further along a jet. Simulated observations confirming the observability of such a phenomenon are conducted, and possible explanations for a reversal in the direction of the Faraday rotation measure gradient are discussed. These results were originally published in Mahmud et al. (2013). Finally, a new error model for the CLEAN algorithm is developed which takes into account correlation between neighbouring pixels. Comparison of error maps calculated using this new model and Monte Carlo maps show striking similarities when the sources considered are well resolved, indicating that the method is correctly reproducing at least some component of the overall uncertainty in the images. The calculation of many useful quantities using this model is demonstrated and the advantages it poses over traditional single pixel calculations is illustrated. The limitations of the model as revealed by Monte Carlo simulations are also discussed; unfortunately, the error model does not work well when applied to compact regions of emission.

Surface quality and surface waves on subwavelength-structured silver films

We analyze the physical-chemical surface properties of single-slit, single-groove subwavelength-structured silver films with high-resolution transmission electron microscopy and calculate exact solutions to Maxwell’s equations corresponding to recent far-field interferometry experiments using these structures. Contrary to a recent suggestion the surface analysis shows that the silver films are free of detectable contaminants. The finite-difference time-domain calculations, in excellent agreement with experiment, show a rapid fringe amplitude decrease in the near zone (slit-groove distance out to 3–4 wavelengths). Extrapolation to slit-groove distances beyond the near zone shows that the surface wave evolves to the expected bound surface plasmon polariton (SPP). Fourier analysis of these results indicates the presence of a distribution of transient, evanescent modes around the SPP that dephase and dissipate as the surface wave evolves from the near to the far zone.

Retrieval of grassland biophysical parameters using multitemporal optical and radar satellite data

The amount and quality of available biomass is a key factor for the sustainable livestock industry and agricultural management related decision making. Globally 31.5% of land cover is grassland while 80% of Ireland’s agricultural land is grassland. In Ireland, grasslands are intensively managed and provide the cheapest feed source for animals. This dissertation presents a detailed state of the art review of satellite remote sensing of grasslands, and the potential application of optical (Moderate–resolution Imaging Spectroradiometer (MODIS)) and radar (TerraSAR-X) time series imagery to estimate the grassland biomass at two study sites (Moorepark and Grange) in the Republic of Ireland using both statistical and state of the art machine learning algorithms. High quality weather data available from the on-site weather station was also used to calculate the Growing Degree Days (GDD) for Grange to determine the impact of ancillary data on biomass estimation. In situ and satellite data covering 12 years for the Moorepark and 6 years for the Grange study sites were used to predict grassland biomass using multiple linear regression, Neuro Fuzzy Inference Systems (ANFIS) models. The results demonstrate that a dense (8-day composite) MODIS image time series, along with high quality in situ data, can be used to retrieve grassland biomass with high performance (R2 = 0:86; p < 0:05, RMSE = 11.07 for Moorepark). The model for Grange was modified to evaluate the synergistic use of vegetation indices derived from remote sensing time series and accumulated GDD information. As GDD is strongly linked to the plant development, or phonological stage, an improvement in biomass estimation would be expected. It was observed that using the ANFIS model the biomass estimation accuracy increased from R2 = 0:76 (p < 0:05) to R2 = 0:81 (p < 0:05) and the root mean square error was reduced by 2.72%. The work on the application of optical remote sensing was further developed using a TerraSAR-X Staring Spotlight mode time series over the Moorepark study site to explore the extent to which very high resolution Synthetic Aperture Radar (SAR) data of interferometrically coherent paddocks can be exploited to retrieve grassland biophysical parameters. After filtering out the non-coherent plots it is demonstrated that interferometric coherence can be used to retrieve grassland biophysical parameters (i. e., height, biomass), and that it is possible to detect changes due to the grass growth, and grazing and mowing events, when the temporal baseline is short (11 days). However, it not possible to automatically uniquely identify the cause of these changes based only on the SAR backscatter and coherence, due to the ambiguity caused by tall grass laid down due to the wind. Overall, the work presented in this dissertation has demonstrated the potential of dense remote sensing and weather data time series to predict grassland biomass using machine-learning algorithms, where high quality ground data were used for training. At present a major limitation for national scale biomass retrieval is the lack of spatial and temporal ground samples, which can be partially resolved by minor modifications in the existing PastureBaseIreland database by adding the location and extent ofeach grassland paddock in the database. As far as remote sensing data requirements are concerned, MODIS is useful for large scale evaluation but due to its coarse resolution it is not possible to detect the variations within the fields and between the fields at the farm scale. However, this issue will be resolved in terms of spatial resolution by the Sentinel-2 mission, and when both satellites (Sentinel-2A and Sentinel-2B) are operational the revisit time will reduce to 5 days, which together with Landsat-8, should enable sufficient cloud-free data for operational biomass estimation at a national scale. The Synthetic Aperture Radar Interferometry (InSAR) approach is feasible if there are enough coherent interferometric pairs available, however this is difficult to achieve due to the temporal decorrelation of the signal. For repeat-pass InSAR over a vegetated area even an 11 days temporal baseline is too large. In order to achieve better coherence a very high resolution is required at the cost of spatial coverage, which limits its scope for use in an operational context at a national scale. Future InSAR missions with pair acquisition in Tandem mode will minimize the temporal decorrelation over vegetation areas for more focused studies. The proposed approach complements the current paradigm of Big Data in Earth Observation, and illustrates the feasibility of integrating data from multiple sources. In future, this framework can be used to build an operational decision support system for retrieval of grassland biophysical parameters based on data from long term planned optical missions (e. g., Landsat, Sentinel) that will ensure the continuity of data acquisition. Similarly, Spanish X-band PAZ and TerraSAR-X2 missions will ensure the continuity of TerraSAR-X and COSMO-SkyMed.