Physicist Marzena Szymanska on the properties of photons, fluids of light and whether it’s possible to make a solid light

If you think of photons, you can maybe wonder why do we not have a complex form made from light. For example. If you have other particles such as electrons, atoms, they form complex structures, they form liquids, they form solids. All the world around us is made from matter which is basically quarks and leptons. But why we cannot make similar things with light? Light is a boson, so in principle we could achieve a fluid of light or even superfluid of light or maybe even a solid of light. So why that has not been possible so far?

So one reason is that photons do not interact: the cross-section between the interaction between two photons is very small and optical frequencies in principle the photons could interact via creation of electron-positron pairs but in practice it doesn’t happen because the process is extremely unlikely. So photons do not interact, and this is one of the limitations why we cannot create complex structures.

Another limitation is that the photons are massless, the mass of photons is zero. For any complex structure that is liquid or solid to be built, there is a competition between kinetic and potential energy, so if photons not have a mass and they don’t interact, we don’t have this notion and we cannot create more complex forms made of photons. However, this can be overcome nowadays, so we can cheat the nature. We can give the photons a mass artificially and we can give photons interactions. So how can we do that?

So to give a photon a mass it’s enough to capture the photons in one direction. If you can create mirrors such that the photons will not escape outside the mirrors, the motion will be frozen in one direction, it will be possible to move in only one direction perpendicular to those mirrors, then effectively in these two other directions it will mean that the photons are massive. This mass will be finite but it will be very small, so it will be in order of 10^{-9} of typical atoms. This is actually quite useful because if the masses are light, then any quantum effect would appear at very high temperatures, even up to room temperatures.

So we can fix the problem of the mass by capturing the photons between two mirrors. The problem of interactions between photons can also be solved if you couple the photons to something of a matter type because if the photons will annihilate and create, let’s say, an exciton or if they couple to some internal degrees of freedom inside an atom, for example, then via that other object the photons will effectively interact. So this was possible to achieve either in semiconductor structures with electron-hole pairs, so excitons, or atoms placed in cavities where interaction between photon could be achieved via coupling to this internal atomic degrees of freedom.

So you could solve these two problems, the mass and the interaction between photons. Because that was possible in experiments to be done, we could make photons interact inside that cavity and in experiment we were able to actually create a fluid of light, so interacting photons with a mass which is very similar to any other fluid and in particular because the mass is so light, it was possible to achieve quantum effect such as, for example, superfluidity at very high temperatures.

So now can stand back a little and ask what is superfluidity. Superfluidity is a state of matter, it’s a new state of matter where microscopic number of particles, a very large number of particles form one object, they behave collectively, they behave together because they occupy the same state. Now, because each atom is not an individual entity, if the atoms (or photons in our case) start flowing, they will flow without any disturbance. A famous example is liquid helium where they can flow up in a container and escape the container: if they flow and they meet an obstacle, they will not scatter. If we look far away from the obstacle, it will look as if our superfluid is not having any resistance to anything, it doesn’t see anything.

So that was possible to be created for photons coupling them to electron-hole pairs in semiconductors forming polaritons. Once the quantum fluid was created, once the superfluid was created, it allowed injection of quite an interesting object: we could put vortices inside such a superfluid, we could inject persistent currents into the superfluid, observation of the frictionless flow was possible. Our photons were doing a very similar thing to what liquid helium or electron-hole pairs in semiconductors, flowing without resistance, not seeing any obstacle on the way and supporting persistent current, supporting vortices.

So then we went a step further in experiments in various groups looking at the transition between a normal state and the superfluid state in the case of these interacting photons. It was possible to see that the transition between a normal state and the superfluid state very similar to the matter particles is happening via creation and annihilation of vortex-anti-vortex pairs, so binding and unbinding those pairs, in the same spirit as Kosterlitz-Thouless transition. So we already had our quantum fluid which now can be used as a laboratory to explore quantum turbulence, to explore behaviour of the vortices, behaviour of the solitons, but now we wanted to go one step further. Now we have a fluid, we have a superfluid, why can not we create a solid out of light?

And that’s a very new area of research at the moment. We can do that, we can create a potential for light. There are various ways of doing that technologically: one can put different pieces of a different material with a different refractive index on the top of our mirrors giving effective potentials for light or can put surface acoustic waves, so modulate the energy of photons via external soundwaves. Instead of having two-dimensional structure one can make one-dimensional lattices out of semiconductor. So there are various ways of creating potentials for photons, and if now you place a photon which has a mass and interactions inside a potential, then you’ll create something that’s just the same as in the case of solid.

Why would we be interested in doing that? As I said, the photons have a very light mass, so the quantum effects are happening at very high temperatures. So now by creating these artificial latices for photons, we can try to model, to quantum simulate some other materials which are much more complicated to study than photons. Moreover, this is already quite an active field in the area of ultracold atoms but ultracold atoms have their limitations. Firstly, they have to be cooled to extremely low temperatures, and here, with photons, we can be almost at the room temperature: that’s one advantage of that system. Another advantage is that the mirrors are never ideal, so there always will be some leakage of photons coming out of these cavities, and by capturing the photons and measuring their energy, their momentum and their position, we know everything about the system inside. So we know not only the ground state, we know also all the excitation spectrum of the system which can be resolved in space. So the amount of information which is given in that system is by far much larger than the information which can be drawn from other platforms, the ultracold atoms, for example.

At the moment the photons inside those lattices are still in a so-called semiclassical level which means that there is a quite number of photons, of polaritons on a one lattices’ side. So now the goal of the field, the open question of the field which is mainly for experimentalists to solve is how to make those latices tight enough so that only one or a few photons can be placed in these lattices so we can explore strongly correlated states with this platform. However, even without that tight confinement already these photons in lattices or polaritons in lattices have been used to look at topological states.

In particular, you can imagine that if you create a in lattice which is very similar to graphene, a honeycomb structure, then what happens is that these materials have very interesting properties. They have a linear dispersion, the so-called Dirac Cone, and the same was possible to achieve in the case of photons. And now, because one can also engineer a spin-orbit coupling in the case of this photonic systems, when we place this photonic system inside a magnetic field, it is possible to open a gap in the spectrum and then create the edge states which will be inside the gap. What it means is that if you have your lattice and you initiate a current which would flow of these photonic particles, if you can achieve topologically protected state, if would mean that if you inject the current in one direction even if it meets some other obstacle, some imperfection at the edge, it would just always low around in one direction, if will now flow in the other direction, there will be no scattering back. So these topological protected states are quite an interest in the community for encoding the information, let’s say, in the direction of that flow.

So basically theses photonic quantum fluids not only allow the realization of superfluidity and the study of the superfluid property such as vortices, quantum turbulence. It’s now moving into the area of quantum simulations where they can be placed in lattices and simulate hopefully strongly correlated stated soon but topological states already.

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