  Observation time is the key parameter for improving the precision of
measurements of gravitational quantum states of particles levitating above a
reflecting surface. We propose a new method of long confinement in such states
of atoms, anti-atoms, neutrons and other particles possessing a magnetic
moment. The Earth gravitational field and a reflecting mirror confine particles
in the vertical direction. The magnetic field originating from electric current
passing through a vertical wire confines particles in the radial direction.
Under appropriate conditions, motions along these two directions are decoupled
to a high degree. We estimate characteristic parameters of the problem, and
list possible systematic effects that limit storage times due to the coupling
of the two motions. In the limit of low particle velocities and magnetic
fields, precise control of the particle motion and long storage times in the
trap can provide ideal conditions for both gravitational, optical and hyperfine
spectroscopy: for the sensitive verification of the equivalence principle for
antihydrogen atoms; for increasing the accuracy of optical and hyperfine
spectroscopy of atoms and antiatoms; for improving constraints on extra
fundamental interactions from experiments with neutrons, atoms and antiatoms.
