Abstract: In this report, we investigate the spin dynamics of a neutron beam in a Stern-Gerlach
experiment. In contrast to the simple constant gradient magnetic field assumed in most
literatures which violates Maxwell Equations, we work with a model of magnetic field
which satises Maxwell Equations. The spin dynamics is investigated by solving the
Schrodinger equation using Fast Fourier Transform method. The spin coherence of the
neutron beam is found to exhibit the humpty-dumpty behaviour[1, 2, 3] even though
there is no
fluctuation to the magnetic field nor any environmental noise. The main
cause of the spin decoherence is identified as the inhomogeneity of the magnetic field in
the x and y components. In addition, the nonlinear terms in the z component of the
magnetic field, zn, n > 1 also contribute to the loss of the spin coherence. Although only
magnetic field model considered is very specific, the cause of the loss of spin coherence
identified using this model is a common features of any realistic magnetic to be used in a
SGA experiment. Therefore the humpty-dumpty nature of the spin coherence exist even
without any
fluctuation to the magnetic field and is inherent to the SGA experiment itself.
Why should it be so difficult to maintain spin coherence? The essential
features of the following qualitative argument are due to Heisenberg.
I won’t try to quote the actual argument, which is on page 3 of the PDF, but it seems that the main problem isn’t entanglement between the particle and the apparatus.
M2: Apparently it’s not possible to recover the original spin, so I guess you just end up with a random spin.
Stern-Gerlach Interferometer with Realistic Magnetic Field:
And see also this earlier paper, Is spin coherence like Humpty-Dumpty? I. Simplified treatment (free full text), which gives a more understandable qualitative argument:
I won’t try to quote the actual argument, which is on page 3 of the PDF, but it seems that the main problem isn’t entanglement between the particle and the apparatus.