Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.

This volume presents the latest advancements and future developments of atomic, molecular and optical (AMO) physics and its vital role in modern sciences and technologies. The chapters are devoted to studies of a wide range of quantum systems, with an emphasis on understanding of quantum coherence and other quantum phenomena originated from light-matter interactions. The book intends to survey the current research landscape and to highlight major scientific trends in AMO physics as well as those interfacing with interdisciplinary sciences. The volume may be particularly useful for young researchers working on establishing their scientific interests and goals.

This work reports on the construction of a new-generation system capable to create single-mode spinor Bose-Einstein condensates of 87Rb, and non-destructively probe them using optical Faraday rotation. This system brings together many of the stateof-the-art technologies in ultra-cold physics in a minimalist design which was possible due to the prolific advances in the field respect to the pioneering experiments (Cornell's, Ketterle's, and Chapman's groups). There is rich phenomena that can be potentially studied in this system from the study of predicted novel quantum phases and topologies to entanglement and spin squeezing which are useful for quantum information and interferometry. The potential of this system make it suitable to answer fundamental questions on the phase transition to a condensed and ferromagnetic state. In particular, this work describes theoretically and experimentally, the atomic spin coherence, which is relevant for applications like coherent sensing of magnetic fields. In this direction, our findings demonstrate the characteristics of our system make it a sensor with the best predicted energy resolution per unit bandwidth (̃10̂-2 h) among all the different technologies applied to magnetometry. The thesis is structured as follows: Part I is dedicated to the mathematical description of the relevant interactions. First, the interaction of optical polarization and atomic spin polarization is reviewed, with special attention to ac-Stark shifts, which are used to generate a conservative trapping potential and Faraday rotation effects that are used for non-destructive spin detection. Second, the interaction of the atoms with a magnetic field is presented. And finally, the mean-filed theory of spinor Bose-Einstein condensation is summarized. The dynamics of a spin-1system in this picture is described by a three-component Gross-Pitaevskii equation. Part II contains three chapters describing the implemented technologies and techniques used in the experiment to create and characterize a spinor condensate. The first chapter describes the ultrahigh vacuum, magnetic fields, lasers, spectroscopy and imaging needed to create a magneto optical trap (MOT) and transfer those atoms into an optical dipole trap (ODT). We implemented a non-standard loading technique based on the semicompensation of the strong differential lightshift induced by the ODT which profits from the effective dark-MOT created at the trap position. In the second chapter we detail, theoretically and experimentally, the all-optical evaporation process employed to achieve condensation in less than five second after the loading. In the final chapter the spin manipulation and read-out techniques are presented. Because there is no observable associated to the spin angle, we exploit the Faraday rotation effect and Stern-Gerlach imaging in order to retrieve information about the spin dynamics. Finally in Part III, we consider the potential of a spinor BEC as a magnetic sensor. The measurement of fundamental properties defining the sensitivity of the sensor are detailed. Those properties are the volume, the temporal coherence and the readout noise. We present a model of the magnetic field environment and its repercussion on the noise of the magnetometer. In the last chapter we present our perspectives to the possible applications of our system.

Following an explosion of research on Bose–Einstein condensation (BEC) ignited by demonstration of the effect by 2001 Nobel prize winners Cornell, Wieman and Ketterle, this book surveys the field of BEC studies. Written by experts in the field, it focuses on Bose–Einstein condensation as a universal phenomenon, covering topics such as cold atoms, magnetic and optical condensates in solids, liquid helium and field theory. Summarising general theoretical concepts and the research to date - including novel experimental realisations in previously inaccessible systems and their theoretical interpretation - it is an excellent resource for researchers and students in theoretical and experimental physics who wish to learn of the general themes of BEC in different subfields.

This thesis presents a theoretical investigation into the creation and exploitation of quantum correlations and entanglement among ultracold atoms. Specifically, it focuses on these non-classical effects in two contexts: (i) tests of local realism with massive particles, e.g., violations of a Bell inequality and the EPR paradox, and (ii) realization of quantum technology by exploitation of entanglement, for example quantum-enhanced metrology. In particular, the work presented in this thesis emphasizes the possibility of demonstrating and characterizing entanglement in realistic experiments, beyond the simple “toy-models” often discussed in the literature. The importance and relevance of this thesis are reflected in a spate of recent publications regarding experimental demonstrations of the atomic Hong-Ou-Mandel effect, observation of EPR entanglement with massive particles and a demonstration of an atomic SU(1,1) interferometer. With a separate chapter on each of these systems, this thesis is at the forefront of current research in ultracold atomic physics.