Bose and Einstein, nanosized

Around two weeks ago I heard about a very interesting article called "Bose-Einstein Condensation in a Plasmonic Lattice." I must admit, the first time I heard about it, I knew what all those words meant separately, but together it was some mumbo jumbo that made no sense to me. What exactly is condensing? Don't these condensates exist only at extremely low temperatures? And what do plasmons have to do with this?

Reading the abstract didn't help at all. Going through the whole article, I understood maybe half of it. But apparently they had done something great, and it was going to be published in Nature Physics!

By chance, I happened to be in contact with one of the authors and he explained everything to me in a way that I finally got what they were doing. And it really was something great.

First of all, what is a Bose-Einstein condensate? About a century ago, Indian scientist Satyendra Nath Bose sent an article to Albert Einstein, humbly asking for his opinion (and for some translation help). Einstein agreed with Bose's theory, translated it to German and sent it to the journal Zeitschrift für Physik.

Bose had derived Planck's law by assuming that the Maxwell-Boltzmann distribution doesn't hold for certain particles, which essentially means that he assumed that photons with the same energy are indistinguishable from each other.

Think about it. If we have two coins, let's say ten cents and fifty cents, and they are thrown in the air so that you can only see the outcome of the flip. Then, there are four possible outcomes: both are heads, both are tails, ten is heads and fifty is tails, or the other way around. But if we have two similar coins, so you can't tell them apart, there are only three possible outcomes: both are heads, both are tails, and one is heads while the other is tails.

In the first scenario, the probability of getting both heads is 1/4, but in the latter, it's 1/3! If the effect of indistinguishability is so great for a small system, then what about physical systems with 10^23 particles per mole?

Einstein realized the implications of this and extended Bose's ideas to matter. Their efforts resulted in the concept of Bose gas, governed by Bose-Einstein statistics. He further proposed that cooling certain atoms to a very low temperature would cause them all to drop down to the ground state, resulting in a new form of matter, known as the Bose-Einstein condensate.

It took almost a century of efforts to confirm the existence of this new state of matter, because of the extremely low temperatures involved. The confirming study in 1995 achieved a temperature of only 170 nK! They measured the velocity distribution of the particles, like in the below picture, where the rising peak indicates that a condensate is forming.

Velocity-distribution for a traditional BEC made up of rubidium atoms.

Bose-Einstein condensates have many peculiar properties, one of the most interesting being that you can describe the whole system with a wave function of a single particle. This is because all of the particle are in the same state.

Now, getting back to the present. When we talk about Bose-Einstein condensation in a plasmonic lattice, what is actually condensing? It's photons, believe it or not.

Then again, how do you achieve condensation of photons? You need to push them to the lowest energy state, but it's not like you can cool them down with liquid helium. And what exactly would be the lowest energy state for a particle that is made up entirely of energy?

This is where the plasmonic lattice comes to play, because it limits the lowest possible energy of the light that is coupled to it. If the photons somehow lose energy in the lattice, there is a certain point after which they will not be allowed to  do so. There exists a ground state in this confining system!

The last problem to tackle is that you need a way to reduce the energy of the photons, without losing the photons in the process. This is a rather tricky problem, but there is a simple solution: add some laser dye into the lattice. The dye is able to absorb and re-emit the photons, but because the efficiency of this process is not 100 %, the light ends up losing energy.

Now, the photons can fall down to the ground state of the system and it's possible to achieve a Bose-Einstein condensate made entirely of light. This kind of condensate has many intriguing properties, but maybe I will talk about that in detail in some other post.

Maybe the coolest thing about all this is that the condensate exists inside a nanophotonic device, which can be fitted on a glass plate the size of a microscope slide. Not to mention that it can be done in room temperature, unlike traditional matter based condensates.

Quite importantly, this research shows that particles don't need to reach the lowest possible energy state for them to form a condensate. It's enough to just have them all confined in a single energy, and that can be anything. However, for matter particles the temperature causes a huge spread in their energies, so in practice matter condensates have to be cooled anyways.

Below is a brilliant video by the researchers at Aalto University, explaining the research in their own words. It's certainly worth checking out!