Coherent spinor dynamics in a spin-1 Bose condensate

Collisions in a thermal gas are perceived as random or incoherent as a consequence of the large numbers of initial and final quantum states accessible to the system. In a quantum gas, e.g. a Bose-Einstein condensate or a degenerate Fermi gas, the phase space accessible to low energy collisions is so restricted that collisions be-come coherent and reversible. Here, we report the observation of coherent spin-changing collisions in a gas of spin-1 bosons. Starting with condensates occupying two spin states, a condensate in the third spin state is coherently and reversibly created by atomic collisions. The observed dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. The spin-dependent scattering length is determined from these oscillations to be -1.45(18) Bohr. Finally, we demonstrate coherent control of the evolution of the system by applying differential phase shifts to the spin states using magnetic fields.Comment: 19 pages, 3 figure

Beyond Gross-Pitaevskii Mean Field Theory

A large number of effects related to the phenomenon of Bose-Einstein Condensation (BEC) can be understood in terms of lowest order mean field theory, whereby the entire system is assumed to be condensed, with thermal and quantum fluctuations completely ignored. Such a treatment leads to the Gross-Pitaevskii Equation (GPE) used extensively throughout this book. Although this theory works remarkably well for a broad range of experimental parameters, a more complete treatment is required for understanding various experiments, including experiments with solitons and vortices. Such treatments should include the dynamical coupling of the condensate to the thermal cloud, the effect of dimensionality, the role of quantum fluctuations, and should also describe the critical regime, including the process of condensate formation. The aim of this Chapter is to give a brief but insightful overview of various recent theories, which extend beyond the GPE. To keep the discussion brief, only the main notions and conclusions will be presented. This Chapter generalizes the presentation of Chapter 1, by explicitly maintaining fluctuations around the condensate order parameter. While the theoretical arguments outlined here are generic, the emphasis is on approaches suitable for describing single weakly-interacting atomic Bose gases in harmonic traps. Interesting effects arising when condensates are trapped in double-well potentials and optical lattices, as well as the cases of spinor condensates, and atomic-molecular coupling, along with the modified or alternative theories needed to describe them, will not be covered here.Comment: Review Article (19 Pages) - To appear in 'Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment', Edited by P.G. Kevrekidis, D.J. Frantzeskakis and R. Carretero-Gonzalez (Springer Verlag

Driven-dissipative non-equilibrium Bose-Einstein condensation of less than ten photons

In a Bose–Einstein condensate, bosons condense in the lowest-energy mode available and exhibit high coherence. Quantum condensation is inherently a multimode phenomenon, yet understanding of the condensation transition in the macroscopic limit is hampered by the difficulty in resolving populations of individual modes and the coherences between them. Here, we report non-equilibrium Bose–Einstein condensation of 7 ± 2 photons in a sculpted dye-filled microcavity, where the extremely small particle number and large mode spacing of the condensate allow us to measure occupancies and coherences of the individual energy levels of the bosonic field. Coherence of the individual modes is found to generally increase with increasing photon number. However, at the break-down of thermal equilibrium we observe phase transitions to a multimode condensate regime wherein coherence unexpectedly decreases with increasing population, suggesting the presence of strong intermode phase or number correlations despite the absence of a direct nonlinearity. Experiments are well-matched to a detailed non-equilibrium model. We find that microlaser and Bose–Einstein statistics each describe complementary parts of our data and are limits of our model in appropriate regimes, providing elements to inform the debate on the differences between the two concepts1,2

Peripheral Signals Conveying Metabolic Information to the Brain: Short-Term and Long-Term Regulation of Food Intake and Energy Homeostasis

Numerous peripheral signals contribute to the regulation of food intake and energy homeostasis. Mechano- and chemoreceptors signaling the presence and energy density of food in the gastrointestinal (GI) tract contribute to satiety in the immediate postprandial period. Changes in circulating glucose concentrations appear to elicit meal initiation and termination by regulating activity of specific hypothalamic neurons that respond to glucose. Other nutrients (e.g., amino acids and fatty acids) and GI peptide hormones, most notably cholecystokinin, are also involved in short-term regulation of food intake. However, the energy density of food and short-term hormonal signals by themselves are insufficient to produce sustained changes in energy balance and body adiposity. Rather, these signals interact with long-term regulators (i.e., insulin, leptin, and possibly the orexigenic gastric peptide, ghrelin) to maintain energy homeostasis. Insulin and leptin are transported into the brain where they modulate expression of hypothalamic neuropeptides known to regulate feeding behavior and body weight. Circulating insulin and leptin concentrations are proportional to body fat content; however, their secretion and circulating levels are also influenced by recent energy intake and dietary macronutrient content. Insulin and leptin concentrations decrease during fasting and energy-restricted diets, independent of body fat changes, ensuring that feeding is triggered before body energy stores become depleted. Dietary fat and fructose do not stimulate insulin secretion and leptin production. Therefore, attenuated production of insulin and leptin could lead to increased energy intake and contribute to weight gain and obesity during long-term consumption of diets high in fat and/or fructose. Transcription of the leptin gene and leptin secretion are regulated by insulin-mediated increases of glucose utilization and appear to require aerobic metabolism of glucose beyond pyruvate. Other adipocyte-derived hormones and proteins that regulate adipocyte metabolism, including acylation stimulating protein, adiponectin, diacylglycerol acyltransferase, and perilipin, are likely to have significant roles in energy homeostasis

Design and Principles of Synchrotrons and Circular Colliders

Lattice design in the context we will describe it here is the design and optimization of the principle elements—the lattice cells—of a circular accelerator, and it includes the dedicated variation of the accelerator elements (as for example position and strength of the magnets in the machine) to obtain well defined and predictable parameters of the stored particle beam. It is therefore closely related to the theory of linear beam optics that has been described in Chap.  2 [1]