Spin – Stern-Gerlach Experiment

The Stern-Gerlach experiment, performed in 1922, delivered the first experimental proof of the fascinating degree of freedom of an electron spin. A beam of silver atoms was generated in an atomic beam furnace. It was then sent towards an inhomogeneous magnetic field. According to classical physics, one would expect the magnetic moments of silver atoms to be randomly oriented. They should be deflected in the inhomogeneous magnetic field by different amounts, depending on their orientation.

However, the researchers observed that the beam was split in two possible states, which were later named spin up and spin down. How can this be explained?

Let us first analyze the electron configuration of a silver atom. One silver atom has a total of 47 electrons. In 46 of these electrons, each spin up is paired with one spin down. The spins neutralize each other. There is only one unpaired spin – the spin of the 5s electron. It can be either in spin up or spin down, or in any superposition of these two states. We can represent this spin state using a Bloch sphere. The spin can point in any random direction.

The spins of all silver atoms are randomly distributed. They are, therefore, not polarised. In fact, there is a close connection between this experiment with a single electron spin and the experiment with single polarized photons.

Here, the polarizing filter corresponds to the inhomogeneous magnetic field. Just like with photons, in a single experiment it is completely random whether the spin points in the direction of the polarizing filter, or in the opposite direction. The result is a black and white random pattern.

Let’s have a closer look at the quantum mechanical measurement process in the Bloch sphere. The spin has some arbitrary orientation before it interacts with the inhomogeneous magnetic field. The inhomogeneous magnetic field acts as a filter. It is presented here as a slot. It forces the spin to take a random orientation, either in line with the inhomogeneous magnetic field, or in the opposite direction. If the basis state is close to “up”, it is very unlikely to change the direction in “down”; however, it may still do so.

When performing their canonical experiment, Stern and Gerlach were unable to use single silver atoms. Therefore, they could not demonstrate the role of chance in each experiment. However, they were the first to demonstrate that the spin is quantized, or separated in “up” and “down”. It was a sensational achievement in their time.