# Excited calcium atoms and photon polarity

This is one of those question where only a few people can contribute an answer, and that answer might be incomprehensible to me, but here goes.

In a very cursory bit on quantum entanglement I need to teach to 18-19 year olds, the book says one of Alain Aspect’s experiments used excited calcium atoms that would emit pairs of photons with a random but equal polarity.

How do we know the photons always have equal polarity when the whole point of the experiment is to show how attempting to discover the polarity gives strange quantum effects?

The physics experts in North America may be asleep at this hour, but I think this one is easy enough for a layman in Asia.

The reason the photons have spins that are exactly opposite (not same) is due to a conservation law. One can confirm that fact experimentally by simply detecting the polarizations with aligned filters. It is when one rotates one of the filters (by any amount not a multiple of 90 degrees ?) that one sees the “paradoxical” result confirming entanglement.

I think this is right. The sun will be shining in North America soon and I stand ready to be corrected…

You rang?

Anyhow, yes, you’re right. Aspect’s experiments used a two-level decay in which the electrons in a calcium atom are excited to some state where they have no net angular momentum. They then emit one photon and shift to an intermediate state, and then emit the second photon and end up in the ground state (which also has no net angular momentum.) Since the first excited state of the atom has zero angular momentum, and the final state has zero angular momentum, then the two photons must together have zero angular momentum; in other words, their angular momenta (i.e., their polarities) are equal and opposite.

What’s not known (and is unknowable) is which photon will have which angular momentum. The two photons have different wavelengths (423 nm and 551 nm.) However, we can’t know until we measure whether the 423-nm photon is spin-up and the 551-nm photon is spin-down, or vice versa, or some superposition of these two states.

This reminds me of one of the peculiarities of the d[sub]xy[/sub] and the d[sub]x^2-y^2[/sub] orbitals. The angular momentum of these orbitals put together is known, but individually, they are unknowable. However, if you were to learn one, you would know that the other is the opposite.

Is this phenomenon somehow related?

I must admit that my knowledge of this is old and probably missing much, but it struck me as peculiar enough to remember.

Thanks. I think I’ll simplify it to my students to: It’s due to conservation laws, and can be verified experimentally.

eh… that doesn’t really do the strangeness of quantum entaglement justice. The MAIN point of quatum entanglement is that before the spins are measured, the photons exist as BOTH spin states. it’s only after the photons are measured do the photons take on opposite spin states.

it’s hard to explain and moreso to digest, but that’s the nature of the quantum beast. stressing that quantum is heavily based on probabilities rather than definites is also another major point you should hammer home so that they don’t leave your class with false foundations. basically, things are ambiguous until proven otherwise.

Just make sure to avoid a Helvitica scenario.