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Polarized high resolution absorption spectra at 4-2 K are reported for single crystals of CszU(Np)O2C1 a and CsU(Np)O,,(NOz)s.Five transitions of the charge-transfer type are observed in both complexes. Zeeman effect measurements give values of g~ in every case. MCD measurements in the nitrate complex permit the unambiguous assignment of a number of excited state symmetries.It is shown by evaluation of the electron-electron repulsion integrals that the excited states are best described as originating from euy),', as opposed to rru s yy', configurations. These configurations are analogous to those describing the charge-transfer states of the uranyl(VI) ion and in some cases the parentage of the neptunyl transitions can be recognized from the polarization of their vibronic structure.

Anderson localisation —the inhibition of wave propagation in disordered media— is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased. Here, we report the results of an experiment measuring the 2D transport of ultracold atoms between two reservoirs, which are connected by a channel containing pointlike disorder. The design overcomes many of the technical challenges that have hampered observation of localisation in previous works. We experimentally observe exponential localisation in a 2D ultracold atom system.

We report on the implementation of a novel optical setup for generating high-resolution customizable potentials to address ultracold bosonic atoms in two dimensions. Two key features are developed for this purpose. The customizable potential is produced with a direct image of a spatial light modulator, conducted with an in-vacuum imaging system of high numerical aperture. Custom potentials are drawn over an area of 600×400 μm with a resolution of 0.9 μm. The second development is a two-dimensional planar trap for atoms with an aspect ratio of 900 and spatial extent of Rayleigh range 1.6 × 1.6 mm, providing near-ballistic in-planar movement. We characterize the setup and present a brief catalog of experiments to highlight the versatility of the system.

Motivated by rapid experimental progress in ultra-cold atomic systems, we aim to provide a simple, intuitive description of Anderson localisation that allows for a direct quantitative comparison to experimental data, as well as yielding novel insights. To this end, we advance, employ and validate a recently-discovered theory -Localisation Landscape Theory (LLT) -which has unparalleled strengths and advantages, both computational and conceptual, over alternative methods. We focus on two-dimensional systems with point-like random scatterers, although an analogous study in other dimensions and with other types of disorder would proceed similarly. We begin by showing that exact eigenstates cannot be efficiently used to extract the localisation length. We then provide a comprehensive review of known LLT, and show that the effective potential of LLT can, to some degree, replace the real potential in the Hamiltonian. Next, we use LLT to compute the localisation length and test our method against exact diagonalisation. Furthermore, we propose a transmission experiment that optimally detects Anderson localisation and link the simulated observations of such an experiment to the predictions of LLT. In addition, we study the dimensional crossover from one to two dimensions, providing a new explanation to the established trends. The prediction of a mobility edge coming from LLT is tested by direct Schrödinger time evolution and is found to be unphysical. Moreover, we investigate expanding wavepackets, and find interesting differences between wavepackets that are initiated within and outside the disorder. We explain these differences using LLT combined with multidimensional tunnelling. Then, we utilise LLT to uncover a connection between the Anderson model for discrete disordered lattices and continuous two-dimensional disordered systems, which provides powerful new insights. From here, we demonstrate that localisation can be distinguished from other effects by a comparison to dynamics in an ordered potential with all other properties unchanged. Finally, we thoroughly investigate the effect of acceleration and repulsive interparticle interactions, as relevant for current experiments.

We experimentally and numerically investigate thermalization processes of a trapped 87 Rb Bose gas, initially prepared in a non-equilibrium state through partial Bragg diffraction of a Bose-Einstein condensate (BEC). The system evolves in a Gaussian potential, where we observe the destruction of the BEC due to collisions, and subsequent growth of a new condensed fraction in an oscillating reference frame. Furthermore, we occasionally observe the presence of defects, which we identify as gray solitons. We simulate the evolution of our system using the truncated Wigner method and compare the outcomes with our experimental results.

While Anderson localisation is largely well-understood, its description has traditionally been rather cumbersome. A recently-developed theory -Localisation Landscape Theory (LLT) -has unparalleled strengths and advantages, both computational and conceptual, over alternative methods. To begin with, we demonstrate that the localisation length cannot be conveniently computed starting directly from the exact eigenstates, thus motivating the need for the LLT approach. Then, we confirm that the Hamiltonian with the effective potential of LLT has very similar low energy eigenstates to that with the physical potential, justifying the crucial role the effective potential plays in our new method. We proceed to use LLT to calculate the localisation length for very low-energy, maximally localised eigenstates, as defined by the length-scale of exponential decay of the eigenstates, (manually) testing our findings against exact diagonalisation. We then describe several mechanisms by which the eigenstates spread out at higher energies where the tunnelling-in-the-effective-potential picture breaks down, and explicitly demonstrate that our method is no longer applicable in this regime. We place our computational scheme in context by explaining the connection to the more general problem of multidimensional tunnelling and discussing the approximations involved. Our method of calculating the localisation length can be applied to (nearly) arbitrary disordered, continuous potentials at very low energies.

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