Incoming links: Planck-Einstein relation
Classic theory predicts that the output frequency must be the same as the input one since the electromagnetic wave makes the electron vibrate with same frequency as itself, which then irradiates further waves.
But the output waves are longer because photons are discrete and energy is proportional to frequency:
The formula is exactly that of two relativistic billiard balls colliding.
Therefore this is evidence that photons exist and have momentum.
Compton Scattering by Compton Scattering (2017)
Source. Experiment with a caesium-137 source.L3.3 Compton Scattering by Barton Zwiebach (2017)
Source. Equation "Hydrogen spectral series mnemonic" gives for example from principal quantum number 1 to 2 a difference:which with Planck-Einstein relation gives about 121.6 nm ( Hz), which is a reasonable match with the value of 121.567... from the NIST Atomic Spectra Database.
No matter how hight the wave intensity, if it the frequency is small, no photons are removed from the material.
This is different from classic waves where energy is proportional to intensity, and coherent with the existence of photons and the Planck-Einstein relation.
Photoelectric effect by UCSB Physics Lecture Demonstrations (2021)
Source. Proportionality factor in the Planck-Einstein relation between light energy and frequency.
And analogously for matter, appears in the de Broglie relations relating momentum and frequency. Also appears in the Schrödinger equation, basically as a consequence/cause of the de Broglie relations most likely.
Intuitively, the Planck constant determines at what length scale do quantum effects start to show up for a given energy scale. It is because the Plank constant is very small that we don't perceive quantum effects on everyday energy/length/time scales. On the , quantum mechanics disappears entirely.
A very direct way of thinking about it is to think about what would happen in a double-slit experiment. TODO think more clearly what happens there.
Defined exactly in the 2019 redefinition of the SI base units to:
Phenomena that produces photons in pairs as it passes through a certain type of crystal.
You can then detect one of the photons, and when you do you know that the other one is there as well and ready to be used. two photon interference experiment comes to mind, which is the basis of photonic quantum computer, where you need two photons to be produced at the exact same time to produce quantum entanglement.
One Photon In, TWO Photons Out by JQInews (2010)
Source. Features Alan Migdall of the National Institute of Standards and Technology. Produced by the Joint Quantum Institute (JQI).
Mentions that this phenomena is useful to determine the efficiency of a single photon detector, as you have the second photon of the pair as a control.
Also briefly describes how the input energy and momentum must balance out the output energy and momentum of the two photons coming out (determined by the output frequency and angle).
Shows the crystal close up of the crystal branded "Cleveland Crystals Inc.". Mentions that only one in a billion photon gets scattered.
Also shows a photomultiplier tube.
Then shows their actual optical table setup, with two tunnels of adjustable angle to get photons with different properties.
How do you produce a single photon? by Physics World (2015)
Source. Very short whiteboard video by Peter Mosley from the University of Bath, but it's worth it for newbs. Basically describes spontaneous parametric down-conversion.
One interesting thing he mentions is that you could get single photons by making your sunglasses thicker and thicker to reduce how many photons pass, but one big downside problem is that then you don't know when the photon is going to come through, that becomes essentially random, and then you can't use this technique if you need two photons at the same time, which is often the case, see also: two photon interference experiment.