Experimental realization of Stern-Gerlach SGy filter

[SpectraCat]

I have been reviewing Sakurai's treatment of the SG experiment by analogy with polarized light, and I realized that I am not sure that I really understand how to construct in a laboratory the $$SG_{y}$$ filter to produce and separate the $$\left|S_{y};\pm\right\rangle$$ states that are analogous to right and left circularly polarized light.

Taking Sakurai's definitions of the lab frame axes (which I believe are standard), the z and x directions are perpendicular to the direction of the beam of atoms, which must therefore define the y-axis in the lab frame. I can imagine creating a magnetic field gradient along the beam direction that will interact with the atoms by drilling holes through the poles of a normal SG magnet pair. What I am unclear on is what precisely happens when a previously prepared beam of atoms in the $$\left|S_{z};+\right\rangle$$ state is passed through this filter. I guess that the two $$\left|S_{y};\pm\right\rangle$$ components of the beam are retarded and accelerated along the beam direction? This would be tricky to observe with a continuous beam, but one could imagine using a pulsed beam, or measuring differential transit times for single atoms to observe this behavior.

So, does anyone know of a reference that describes this experiment (I assume it has been conducted in some form)? Or have I made a mistake somewhere in my predictions of what would happen?

 

[Maxim Zh]

I guess that the two $$\left|S_{y};\pm\right\rangle$$ components of the beam are retarded and accelerated along the beam direction?

It looks like different refraction coefficients. So oblique incidence could help.

Let's consider a particle with magnetic moment

$$\mathbf{m} = (0, m_y, 0),$$

which is in nonhomogeneous magnetic field

$$\mathbf{H} = (H_0(x+y), H_0(x+y), 0).$$

Then the force will be

$$\matbf{F} = (\mathbf{m} \nabla)\matbf{H} = m_y\frac{\partial}{\partial y}\matbf{H} =<br /> H_0 m_y(1, 1, 0).$$

The beam deviation along the x-axis depends on magnetic moment direction.

But such magnetic field will also turn the dipoles. In quantum mechanics it's equivalent to a perturbation which can stimulate a spin state change.