I have been playing around with the maths for some simple quantum systems recently. A lot of systems model operations performed on a qubit as rotations in three dimensions (The Bloch Sphere).

Around the same time, I was playing with polarized light, and pretty much all complicated optical devices (such as quarter wave plates, faraday rotators, electro-optical modulators and more) can be modelled as rotations (The Poincare Sphere)

(Side note: Both these spheres don’t directly represent any dimensions in the real world. They’re just mapping things that can vary in three dimensions, and have a conserved quantity such if you use Pythagoras’s theorem to add their lengths in three dimensions it always sums to one. Or, in other words, a unit sphere).

After thinking about it for a while, I kind of got it, but I got sick not having something tangible to play with. Here’s my attempt at something visual and tangible, and cheap for others to make.

The trick was finding a good source of acrylic spheres. Turns out bath bomb moulds are perfect. You can pick them up on ebay for a few dollars each. The magic phrase to search for would be “120mm bath bomb mould”.

(I’ll also apologise in advance for the photos here. Taking good closeup pictures of transparent domes is pretty difficult, and these are as good as I could get in an hour of fiddling with tents and lighting. )

The Bloch sphere:

The Poincare sphere, with the direction of polarizations shown. The labels are: Horizontal, Vertical on the S1 axis, Diagonal (45*) and Anti-Diagonal (-45*) on the S2 axis, and Right and Left Circular on the S3 axis. I believe I’ve matched the standard layout and right-hand-rules such that it can be used in a class without any changes.

And I also made a version with text labels ( H, V, D, A, R, L) to avoid any ambiguity with the perceived direction of the arrows based on the direction you look at it:

Files are here for anyone that’s interested:

https://www.thingiverse.com/thing:3053421

If you make one please let me know, I’d love to see a pic