The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.

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Two distinct mechanisms are investigated for transferring a pure 87 Rb Bose-Einstein condensate in the |F = 2, m F = 2〉 state into a mixture of condensates in all the m F states within the F = 2 manifold. Some of these condensates remain trapped whilst others are output coupled in the form of an elementary pulsed atom laser. Here we present details of the condensate preparation and results of the two condensate output coupling schemes. The first scheme is a radio frequency technique which allows controllable transfer into available m F states, and the second makes use of Majorana spin flips to equally populate all the manifold sub-states. More recently, the production of multi-component condensates has revealed intriguing quantum fluid dynamics, and enabled precise measurement of relative quantum phase [9]. Experiments at JILA have focused on mixtures involving atoms in different ground state hyperfine levels (quantum number F), and coupling with a two photon (microwave plus radio frequency) transition. Experiments at MIT have used an optical dipole trap to confine a condensate occupying all magnetic sub-states (quantum number m F ) of the same hyperfine level [10]. Spin exchange processes result in domain formation which exhibits an anti-ferromagnetic interaction [11]. An important aspect of that work is the confinement of condensed atoms in sub-states which cannot be magnetically trapped.In this paper we present the results of two techniques for transforming a single state |F = 2, m F = 2〉 87 Rb Bose condensate into a mixture of all five magnetic sub-states of the F = 2 hyperfine level. Two of these states are magnetically confined (|2, 2〉 and |2, 1〉), with magnetic moments differing by a factor of 2, and the other states are unconfined.Applying an RF field similar to that used in the evaporative cooling stage of the experiment we can couple atoms between adjacent m F states. It is possible to control the number of atoms which are coupled from the |2, 2〉 state into the other m F states: condensates with predetermined sub-state populations can be constructed. For example, we can limit the transfer into untrapped states.

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