Spatial and energetic mode dynamics of cold atomic systems

In this thesis we relate the formal description of various cold atomic systems in the energy eigenbasis, to the observable spatial mode dynamics. Herein the `spatial mode dynamics' refers to the direction of photon emission following the spontaneous emission of an excited fermion in the presence of a same species and spin ideal anisotropic Fermi sea in its internal ground state. Due to the Pauli principle, the presence of the ground state Fermi sea renders the phase space, anisotropic and only partially accessible, thereby a ecting the direction of photon emission following spontaneous emission. The spatial and energetic mode dynamics also refers to the quantum `tunneling' interaction between localised spatial modes, synonymous with double well type potentials. Here we relate the dynamics of the wavefunction in both the energetic and spatial representations. Using this approach we approximate the relationship between the spatial and energetic representations of a wavefunction spanning three spatial and energetic modes. This is extended to a process known as Spatial Adiabatic Passage, which is a technique to transport matter waves between localised spatial modes. This approach allows us to interpret the transport of matter waves as a signature of a geometric phase acquired by the one of the internal energy eigenstates of the system during the cyclical evolution. We further show that this geometric phase may be used to create spatial mode qubit and qutrit states.

Techniques for engineering quantum states

In this thesis I theoretically study quantum states of ultracold atoms. The majority of the Chapters focus on engineering specific quantum states of single atoms with high fidelity in experimentally realistic systems. In the sixth Chapter, I investigate the stability and dynamics of new multidimensional solitonic states that can be created in inhomogeneous atomic Bose-Einstein condensates. In Chapter three I present two papers in which I demonstrate how the coherent tunnelling by adiabatic passage (CTAP) process can be implemented in an experimentally realistic atom chip system, to coherently transfer the centre-of-mass of a single atom between two spatially distinct magnetic waveguides. In these works I also utilise GPU (Graphics Processing Unit) computing which offers a significant performance increase in the numerical simulation of the Schrödinger equation. In Chapter four I investigate the CTAP process for a linear arrangement of radio frequency traps where the centre-of-mass of both, single atoms and clouds of interacting atoms, can be coherently controlled. In Chapter five I present a theoretical study of adiabatic radio frequency potentials where I use Floquet theory to more accurately model situations where frequencies are close and/or field amplitudes are large. I also show how one can create highly versatile 2D adiabatic radio frequency potentials using multiple radio frequency fields with arbitrary field orientation and demonstrate their utility by simulating the creation of ring vortex solitons. In the sixth Chapter I discuss the stability and dynamics of a family of multidimensional solitonic states created in harmonically confined Bose-Einstein condensates. I demonstrate that these solitonic states have interesting dynamical instabilities, where a continuous collapse and revival of the initial state occurs. Through Bogoliubov analysis, I determine the modes responsible for the observed instabilities of each solitonic state and also extract information related to the time at which instability can be observed.