I don't think the author of this piece has a clue how this works. I certainly don't, even after reading it slowly.
The details are probably fiddly though.
- what is a "photon gas"? Is this a state of matter? What is the matter if photons aren't matter?
- ideal gas law, PV=nRT not obeyed? Due to ionization or something? Photon pressure?
- Joule-Thompson Effect?
- Building computers out of light?
- Which thermodynamic properties or laws are being obeyed? Is this something like a Carnot cycle, but with photons?
If you can control the nonlinearity, you can control the wavelength change and so change properties such as the angle of refraction to change where the light goes (like in a rainbow/a prism, where the red light refracts more).
They let the photon gas move around inside a crystal where they behave nonlinearly so that photons are bound or repelled to some degree, so that they behave more like CO2 or a refrigerant than like helium.
It's yet another misleading use of the word "photon". A photon gas basically refers to the statistical behaviour of quantised oscillators (typically some atoms/molecules that can vibrate) in the walls of a closed box, called a "cavity". Since the oscillators de-excite by emitting radiation which stays inside the box until it's re-absorbed by the oscillators, you can sort of get away with thinking of it like the distribution of the modes of oscillations of the electromagnetic fields inside the cavity, which is what photons actually are.