A study of the equilibrium positions of a superconducting magnetic levitation system which substitutes an electromagnetic energy for a mechanical energy is in progress for the absolute determination of the magnetic flux quantum «1>0' The study on a preliminary system at ppm-level resolution has been done and the reproducibility of the trajectory turned out to be of the order of 10 ppm. The problems of the present system and ideas for the next system at the sub-ppm level are discussed.(2) corner cube reflector Laser Interferometerwhere k is the flux-to-current conversion factor and n; is the order of the SQUID.The vertical position z, of the center of gravity of M is measured by a laser interferometer. Sets of data (ie' z.) as a function of cI> describe the equilibrium trajectory of the system. It is assumed that there exists a unique equilibrium trajectory as long as the attitude of M is stable and the Meissner effect of the system holds.The total energy U of the system is the sum of the magnetic energy of the system and the gravitational potential energy of M. The difference in U between two points (epf, i el , Zel) and (cI>h, i eh , Zeh) arises from the energy supplied by the current driver I d during the flux-up from cI>l to 4>h. This energy injected under a quasi-static flux-up condition can be obtained by the integration of i e over cI>I to cI>h on the equilibrium trajectory, sõ 4>h i e dcI> = ! (cI>h i eh -cI>li el) + mg (Zeh -Zel) (3) 4>[ where g is the gravitational acceleration.Introducing the expressions for cI> and i e in terms of 4>0 Fig. 1. Superconducting magnetic levitation system.The body M is levitated by the force due to the Meissner effect when cI> is large enough. When cI> is kept constant (is = 0), M reaches the equilibrium position which depends on cI>.The system in equilibrium will now be dealt with, and quantities in equilibrium are indicated with the suffix "e." The coil current i, is measured by a SQUID ammeter (CSQ) which is calibrated with a Josephson voltage reference and a calibrated resistor aswhere N is the number of cI>0 linking C. II. THEORYA superconducting magnetic levitation system is composed of a superconducting floating body M with mass m, a superconducting coil C, and the Josephson junction J irradiated with a microwave frequency 1as shown in Fig. 1. The flux cI> linking C increases when the bias current is of J is set on the first Shapiro step ( V] = 1cI>0) by the drive current i d controlled by the SQUID ammeter (VSQ) so that the EMF of C corresponds to 1cI>0.This process may be called flux-up, and cI> is obtained by the integration oflover the flux-up period T as

A study on a new method of determining the magnetic flux quantum φ0 possibly at subppm level using a superconducting levitation system is described with some data from a preliminary experiment. The method employs a superconducting levitation system to substitute the gravitational potential energy of the floating body for the magnetic energy. The estimation of the expected accuracy and methods of improving the experiment are discussed.

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Precision measurements at the National Research Laboratory of Metrology used to determine fundamental constants and to test physical theory are described: they are related to the determination of silicon lattice spacing; the magnetic flux quantum; and a search for the fifth force. Equipment and techniques for nanometrology are described in terms of the nanoscale, nanoguide and nanodrive, all of which have immediate applications in advanced technology. An example is introduced which demonstrates the power of the scanning tunnelling microscope (STM) in nanometrology.