A Hybrid Lagrangian Variational Method for Bose–Einstein Condensates in Optical Lattices

Solving the Gross–Pitaevskii (GP) equation describing a Bose–Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions of the GP equation for systems where the external potential exhibits rapid variation along one spatial direction. Examples of such systems include a BEC subjected to a one-dimensional optical lattice or a Bragg pulse. This variational method is a hybrid form of the Lagrangian variational method for the GP equation in which a hybrid trial wavefunction assumes a Gaussian form in two coordinates while being totally unspecified in the third coordinate. The resulting equations of motion consist of a quasi-one-dimensional GP equation coupled to ordinary differential equations for the widths of the transverse Gaussians. We use this method to investigate how an optical lattice can be used to move a condensate non-adiabatically

A Hybrid Lagrangian Variation Method for Bose-Einstein Condensates in Optical Lattices

Solving the Gross--Pitaevskii (GP) equation describing a Bose--Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions of the GP equation for systems where the external potential exhibits rapid varation along one spatial direction. Examples of such systems include a BEC subjected to a one--dimensional optical lattice or a Bragg pulse. This variational method is a hybrid form of the Lagrangian Variational Method for the GP equation in which a hybrid trial wavefunction assumes a gaussian form in two coordinates while being totally unspecified in the third coordinate. The resulting equations of motion consist of a quasi--one--dimensional GP equation coupled to ordinary differential equations for the widths of the transverse gaussians. We use this method to investigate how an optical lattice can be used to move a condensate non--adiabatically.Comment: 16 pages and 1 figur

Development and analyses of hybrid imaging systems

The aim of the work reported in this thesis is to analyse and develop hybrid imaging systems. Hybrid imaging systems are electro-optical imaging systems with optical elements implemented in the aperture-stop and digital post-image processing applied to the acquired image, jointly optimised for task-based imaging. Extended depth-of-field is one of the benefits that hybrid imaging systems provide. In particular, and as main objective of this thesis, we analyse and develop a hybrid and compact optical zoom lens with a single moving element and extended-depth-of-field. We show how a specific hybrid imaging technique can be used and implemented to miniaturise these zoom lenses such that they can be implemented in a mobile phone. We demonstrate that the implementation of a given phase mask and digital image restoration of the recorded images can imply two important trade-offs, namely image artifacts and noise amplification in the restored images. Image artifacts have not been given much attention in hybrid imaging systems. Despite of this, the image artifacts have probably been the main reason why no commercial products have been manufactured until now. In this thesis, we analyse for the first time the form of specific image artifacts, which imply that we are able to fully understand the physics of the artifacts. Based on the understanding, we develop a technique to remove the image artifacts. Furthermore, we develop a hybrid imaging system with adjustable noise amplification. Our original contributions to hybrid imaging techniques, which include the understanding of depth-of-field in various hybrid imaging systems (with and without sampling), understanding and development of a compact zoom lens with a single moving element, the understanding and removal of image artifacts, and development of a hybrid imaging system with adjustable noise amplification, will make the development of future and commercial hybrid imaging systems possible