Abstract

In recent years remarkable success was achieved in trapping neutral particles with a magnetic moment such as neutrons, hydrogen and sodium using static magnetic fields.^[1] In all these experiments particles were trapped in a local minimum of the magnetic field, the spin antiparallel to the field. Even though the classical Earnshaw theorem forbids the creation of a local maximum of the magnetic field in free space, a maximum be achieved around a region of non zero current. An atom with spin S and magnetic moment μ experiences in the magnetic field of a current carrying wire (Fig. 1) a potential $\text{V}=-\mu SB\propto \frac{1}{\text{r}}$. This potential is attractive for the spin parallel to the magnetic field. For the spin (magnetic moment) to follow adiabatically the magnetic field its, Larmor precession (ω_L) has to be much faster than the perceived rotation of the magnetic field the atom sees in its rest frame (ω_O). For cicular like orbits one can show that $\frac{{\omega }_{\text{L}}}{{\omega }_{\text{O}}}=l$, where 1 is the angular momentum quantum number. A simple estimate of the lifetime τ of these states to spin flip transitions can be made using an argument given by Güttiger^[2]: $\tau ~\frac{l^2}{{\omega }_{\text{O}}}$.

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