## Liquid Light

Elisabeth Giacobino works at the Ecole Normale Supérieure in Paris. Last week she gave a talk at the Centre for Quantum Technologies. It was about ‘polariton condensates’. You can see a video of her talk here.

What’s a polariton? It’s a strange particle: a blend of matter and light. Polaritons are mostly made of light… with just enough matter mixed in so they can form a liquid! This liquid can form eddies just like water. Giacobino and her team of scientists have actually gotten pictures:

Physicists call this liquid a ‘polariton condensate’, but normal people may better appreciate how wonderful it is if we call it liquid light. That’s not 100% accurate, but it’s close—you’ll see what I mean in a minute.

Here’s a picture of Elisabeth Giacobino (at right) and her coworkers in 2010—not exactly the same team who is working on liquid light, but the best I can find:

#### How to make liquid light

How do you make liquid light?

First, take a thin film of some semiconductor like gallium arsenide. It’s full of electrons roaming around, so imagine a sea of electrons, like water. If you knock out an electron with enough energy, you’ll get a ‘hole’ which can move around like a particle of its own. Yes, the absence of a thing can act like a thing. Imagine an air bubble in the sea.

All this so far is standard stuff. But now for something more tricky: if you knock an electron just a little, it won’t go far from the hole it left behind. They’ll be attracted to each other, so they’ll orbit each other!

What you’ve got now is like a hydrogen atom—but instead of an electron and a proton, it’s made from an electron and a hole! It’s called an exciton. In Giacobino’s experiments, the excitons are 200 times as big as hydrogen atoms.

Excitons are exciting, but not exciting enough for us. So next, put a mirror on each side of your thin film. Now light can bounce back and forth. The light will interact with the excitons. If you do it right, this lets a particle of light—called a photon—blend with an exciton and form a new particle called polariton.

How does a photon ‘blend’ with an exciton? Umm, err… this involves quantum mechanics. In quantum mechanics you can take two possible situations and add them and get a new one, a kind of ‘blend’ called a ‘superposition’. ‘Schrödinger’s cat’ is what you get when you blend a live cat and a dead cat. People like to argue about why we don’t see half-live, half-dead cats. But never mind: we can see a blend of a photon and an exciton! Giacobino and her coworkers have done just that.

The polaritons they create are mostly light, with just a teeny bit of exciton blended in. Photons have no mass at all. So, perhaps it’s not surprising that their polaritons have a very small mass: about 10-5 times as heavy as an electron!

They don’t last very long: just about 4-10 picoseconds. A picosecond is a trillionth of a second, or 10-12 seconds. After that they fall apart. However, this is long enough for polaritons to do lots of interesting things.

For starters, polaritons interact with each other enough to form a liquid. But it’s not just any ordinary liquid: it’s often a superfluid, like very cold liquid helium. This means among other things, that it has almost no viscosity.

So: it’s even better than liquid light: it’s superfluid light!

#### The flow of liquid light

What can you do with liquid light?

For starters, you can watch it flow around obstacles. Semiconductors have ‘defects’—little flaws in the crystal structure. These act as obstacles to the flow of polaritons. And Giacobimo and her team have seen the flow of polaritons around defects in the semiconductor:

The two pictures at left are two views of the polariton condensate flowing smoothly around a defect. In these pictures the condensate is a superfluid.

The two pictures in the middle show a different situation. Here the polariton condensate is viscous enough so that it forms a trail of eddies as it flows past the defect. Yes, eddies of light!

And the two pictures at right show yet another situation. In every fluid, we can have waves of pressure. This is called… ‘sound’. Yes, this is how ordinary sound works in air, or under water. But we can also have sound in a polariton condensate!

That’s pretty cool: sound in liquid light! But wait. We haven’t gotten to the really cool part yet. Whenever you have a fluid moving past an obstacle faster than the speed of sound, you get a ‘shock wave’: the obstacle leaves an expanding trail of sound in its wake, behind it, because the sound can’t catch up. That’s why jets flying faster than sound leave a sonic boom behind them.

And that’s what you’re seeing in the pictures at right. The polariton condensate is flowing past the defect faster than the speed of sound, which happens to be around 850,000 meters per second in this experiment. We’re seeing the shock wave it makes. So, we’re seeing a sonic boom in liquid light!

It’s possible we’ll be able to use polariton condensates for interesting new technologies. Giacobimo and her team are also considering using them to study Hawking radiation: the feeble glow that black holes emit according to Hawking’s predictions. There aren’t black holes in polariton condensates, but it may be possible to create a similar kind of radiation. That would be really cool!

But to me, just being able to make a liquid consisting mostly of light, and study its properties, is already a triumph: just for the beauty of it.

#### Scary technical details

All the pictures of polariton condensates flowing around a defect came from here:

• A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemenager, R. Houdre, E. Giacobino, C. Ciuti, and A. Bramati, Hydrodynamic solitons in polariton superfluids.

and this is the paper to read for more details.

I tried to be comprehensible to ordinary folks, but there are a few more things I can’t resist saying.

First, there are actually many different kinds of polaritons. In general, polaritons are quasiparticles formed by the interaction of photons and matter. For example, in some crystals sound acts like it’s made of particles, and these quasiparticles are called ‘phonons’. But sometimes phonons can interact with light to form quasiparticles—and these are called ‘phonon-polaritons’. I’ve only been talking about ‘exciton-polaritons’.

If you know a bit about superfluids, you may be interested to hear that the wavy patterns show the phase of the order parameter ψ in the Landau-Ginzburg theory of superfluids:

If you know about quantum field theory, you may be interested to know that the Hamiltonian describing photon-exciton interactions involves terms roughly like

$\alpha a^\dagger a + \beta b^\dagger b + \gamma (a^\dagger b + b^\dagger a)$

where $a$ is the annihilation operator for photons, $b$ is the annihilation operator for excitons, the Greek letters are various constants, and the third term describes the interaction of photons and excitons. We can simplify this Hamiltonian by defining new particles that are linear combinations of photons and excitons. It’s just like diagonalizing a matrix; we get something like

$\delta c^\dagger c + \epsilon d^\dagger d$

where $c$ and $d$ are certain linear combinations of $a$ and $b$. These act as annihilation operators for our new particles… and one of these new particles is the very light ‘polariton’ I’ve been talking about!

### 30 Responses to Liquid Light

1. A. Nonymous says:

Since 2002, Elisabeth Giacobino is not anymore director of physics and math at the CNRS.

• John Baez says:

Thanks! I had trouble getting up-to-date information.

2. Tim van Beek says:

The analogy between the equations describing the excitations of a Bose-Einstein condensate (BEC – a peculiar state of matter exhibiting quantum properties at macroscopic scales) and the metrics of the curved space-time has been noticed about a decade ago…

Ugh, somehow I completely missed that…I think I should check out just how deep that analogy is, but according to the authors:

A great research effort in this domain has recently culminated with the observation of stimulated Hawking emission in water [12].

Which refers to actual experiments, not numerical simulations. So maybe Hawking may get his Nobel prize after all. Although it is kind of uncool to talk about the transition from subsonic to supersonic flow as an event horizon :-) and that

emission of Hawking phonons means correlated density perturbations propagating on both sides of the horizon.

A real glowing black hole in a laboratory would be so much more fun, but I guess one could use the model and the graphics of the paper in order to explain the original Hawking radiation in a QFT class…

• John Baez says:

Tim wrote:

… it is kind of uncool to talk about the transition from subsonic to supersonic flow as an event horizon :-)

I don’t think it’s so bad. It’s true that this analogy violates the esthetics of people working on general relativity, but a lot of the same phenomena show up.

I saw a nice example in a fountain in Vienna once. Water flows smoothly down a channel, faster and faster, until it pours off the edge in a small waterfall. If you tap the water’s smooth surface with your finger, a wave goes out. In the region where the water flows more slowly than the speed of this wave, it goes out in all directions—but faster downstream than upstream. In the region where the water flows faster than the speed of this wave, the whole wave is carried downstream: no information propagates upstream. Between these regions there is a boundary: an ‘event horizon’. No information from water waves can get out of this event horizon. (Well, at least that’s true for waves of small amplitude and certain frequencies.) So it acts a bit like a black hole.

And the really interesting thing is that if you quantize this problem, you’ll get Hawking radiation! Roughly speaking, wave-antiwave pairs will form right near the event horizon, thanks to quantum fluctuations, and some of the waves will escape upstream!

People sometimes call the sound analogue of a black hole a dumb hole, not because the analogy is stupid, but because ‘dumb’ also means ‘unable to speak’. (I guess ‘mute hole’ would be a politically correct substitute.)

Ted Jacobson is always very clear, so in my attempt to find you a nice paper on Hawking radiation and liquid helium I immediately turned to one by him:

• T.A. Jacobson, G.E. Volovik, Event horizons and ergoregions in 3He, 10.1103/PhysRevD.58.064021.

The only conceivable experimental consequences of Hawking radiation at present would arise from evaporation of a (hypothetical) population of primordial black holes.

For this reason models simulating event horizons in condensed matter can be useful. The first attempt at a model of this kind was made with a moving liquid [3–5]. The propagation of sound waves on the background of a moving inhomogeneous liquid is similar to the propagation of light in (3+1)-dimensional Lorentzian geometry, and is governed by the relativistic wave equation:

$\partial_\mu (\sqrt{-g} g^{\mu \nu} \partial_\nu \Psi) = 0$

The ‘acoustic’ metric $g^{\mu \nu}$ , in which the sound wave is propagating, is determined by the inhomogeneity and local flow velocity of the liquid. If the liquid moves supersonically
a sonic ‘event horizon’ can arise. A drawback of this model for the simulation of black hole physics is that ordinary liquids are essentially dissipative systems and are very far from the condition where quantum effects can be of any importance: this smears the effects that, like the Hawking effect, are related to quantum fluctuations.

Better candidates are superfluids, which allow nondissipative motion of the vacuum (superfluid condensate, or ground state), and which also support well defined elementary excitations that propagate in a ‘curved space’ of the inhomogeneous moving condensate. The Fermi superfluids (including superconductors) are appealing candidates because their low temperature dynamics are described by quantum field theories similar to those in high energy physics [6]. Among them superfluid 3He-A has the advantage that this superfluid supports an effective gravity caused by some components of the superfluid order parameter [7].

There is one important obstacle to the formation of an horizon in a moving condensate: superfluidity collapses, i.e. the condensate disappears, before the corresponding speed of light is reached. For example in superfluid 4He the Landau velocity at which the condensate is unstable to roton excitation is smaller than the speed of sound and thus the supersonic flow can not be established. For fermionic systems the collapse of superfluid/superconducting state due to “superluminal” motion of the condensate was discussed in [8]. Therefore we have looked for a model in which the condensate is at rest with respect to the container We show here that a ‘superluminally’ moving inhomogeneity of the order parameter (soliton, vortex or other texture) in superfluid 3He-A provides such a model and can simulate the physics of an event horizon and ergoregion for ‘relativistic’ massless fermions—the Bogoliubov-Nambu quasiparticles.

Tim wrote

A great research effort in this domain has recently culminated with the observation of stimulated Hawking emission in water [12].

Which refers to actual experiments, not numerical simulations.

Another
macroscopic trial.

3. John Huerta says:

You write:

one of these new particles is the very light ‘polariton’ I’ve been talking about!

So, what’s the other one?

• John Baez says:

John wrote:

So, what’s the other one?

She didn’t talk about it beyond showing a graph of the dispersion relation (energy as a function of momentum) for both quasiparticles. However, since these quasiparticles are formed by applying a unitary transformation to the photon and exciton states, and the polariton is mostly photon with just a little exciton added in, this other quasiparticle must be a mostly exciton with just a little photon added in (or subtracted off, if you like).

I guess this other one less dramatic. Changing the mass of the photon slightly, and giving it nonlinear interactions with other photons, is a big deal. Changing the mass of the exciton slightly, and changing its nonlinear interaction with other excitons, is probably not.

4. JMS says:

Great physics. However note that Elisabeth Giacobino is no longuer director of physics and maths at CNRS — actually there is no longuer a director of physics and maths, there is rather a director of physics (Bertrand Girard) and one for maths (Guy Métivier).

• John Baez says:

Thanks—I’ve corrected this. Unfortunately all the online information I could find was outdated, and I couldn’t find a personal web page for her. The mistake of calling CNRS a ‘research institute’ was just foolishness on my part, since I knew better.

5. Ephraim Gandolf says:

CNRS is the French funding agency, like NSF in the US. Not a “big research center”. This however goes well with the rest of the article…

• John Baez says:

Umm, thanks. I decided to write this in a popular style because I think this work deserves to be known by a wider audience. But that doesn’t excuse errors.

6. John Baez says:

Over on Google+, Fabrice Laussy wrote:

Actually polariton people do not usually like to think of their polaritons as light (concepts of liquid light predate those of polariton superfluids & polariton condensates). It’s a recurrent criticism from the pure exciton community (where there’s condensation of the exciton field only) that polaritons are coherent because of their photon fraction, and that adding the exciton to make the light counterpart interact spoils its coherence. That is, exciton people say “polaritons are light”, in a negative way. So all the better if polaritons as “liquid light” are now regarded as the beautiful thing (the outstanding claim of polaritons is that they Bose-condense at room temperature; with recent claims of “Bose condensation of light” as well, however, them being light or not recedes into semantics).

7. Speed says:

” … the speed of sound, which happens to be around 850,000 meters per second in this experiment.”

That number seems high.

• Todd Trimble says:

Why? I guess you know that the speed of sound varies greatly from one medium to another. For example, the speed of sound in a steel rod is about 6000m/s, about 17 or 18 times faster than the speed of sound in dry air at room temperature. It wouldn’t surprise me that for such unusual states of “matter” like “liquid light”, the speed of sound could be very much higher.

• John Baez says:

Rigid things like steel have faster speeds of sound than fluids like air or water, almost by definition of ‘rigid’. But this polariton condensate, while fluid, is so strange that I have no intuition for how fast sound should move through it. I just got the number 8.5 × 105 meters/second from Giacobino’s talk—or more precisely, my notes from her talk—without thinking about it.

So, let’s see. Looking at the paper, I find to my mild annoyance that while they give a general formula for the speed of sound in a polariton condensate, they don’t say what that speed was in any of their experiments. However, they do day that they got the polariton condensate to flow at a speed of 1.7 micrometers per picosecond—using units for very tiny, very quick people. A micrometer per picosecond is 106 meters per second, if I haven’t screwed up.

Since they were trying to create a nicely visible ‘sonic boom’, they needed the condensate to flow just a bit faster than the speed of sound. (If it went a lot faster than the speed of sound, we would not see a nice shock wave going out at roughly a 45° angle.)

So, 8.5 × 105 meters/second sounds about right for the speed of sound in their polariton condensate.

By comparison, the speed of sound in air—I had to look this up—is a measly 342 meters/second.

If I wanted to understand this further I’d go to the paper and look up the reference where they give the formula for the speed of sound in a polariton condensate!

• John Baez says:

Since the polariton condensate is a superfluid, I thought I’d look up the speed of sound in another superfluid: liquid helium-4. At near absolute zero, the speed of sound in that substance is just 238 meters/second.

So, not very high; nothing to help me understand why it’s so high in the polariton condensate! But the same formula as in Giacobino’s paper should apply, since that formula is based on the Landau–Ginzburg model of superfluidity, which also applies to liquid helium. (Anyone who likes quantum field theory should enjoy this stuff, since the Landau–Ginzburg model is a U(1) gauge theory with spontaneously broken symmetry, somewhat similar to the Higgs mechanism.)

By the way: besides ordinary sound, or ‘first sound’, superfluid helium also supports other kinds of waves. ‘Second sound’ is a pulse of heat: heat in a superfluid travels in waves rather than by diffusion! ‘Third sound’ consists of waves on the surface of superfluid helium adsorbed onto a surface. (‘Adsorbed’ is one of those wonderful words that makes you sound either like a real know-it-all or someone who can’t spell.) And ‘fourth sound’, well, I understand that even less! Apparently it’s a kind of pressure and density wave that only the superfluid component takes part in, when you’ve got a mix of ordinary liquid helium and superfluid helium.

• Frederik De Roo says:

Isn’t there a square root of the inverse mass of the polariton in the formula?

Being half light-half matter quasiparticles, they posses an extremely small mass $m_{pol}$ on the order of $10^{-8}$ times the H mass.

• John Baez says:

I’ll take your word for it! So everything else being equal (which it’s probably not), since the polariton is roughly 108 times lighter than a helium atom, we’d expect sound to travel roughly 104 faster in a polariton condensate than in superfluid helium. We saw that the speed of sound in superfluid helium is about 250 meters per second. So, we’d expect sound to go roughly 2.5 × 106 meters/second in the polariton condensate.

The actual speed is 8.5 × 105 meters/second. That’s pretty close!

• Todd Trimble says:

My ‘why’ (do you think the number sounds high?), addressed to the commenter Speed, was not based on my having any idea why it was that high, but on knowing no good reason for thinking it couldn’t be that high. But John has meanwhile dug up some interesting facts; I was also vaguely wondering about superfluidity, but it sounds as if that’s a red herring.

• John Baez says:

Well, now I’m thinking the superfluidity is not a red herring; perhaps just pink. From what Frederik said above, and my back-of-the-envelope calculations, my guess is that for a bunch of superfluids the speed of sound is largely accounted for by the fact that it’s proportional to the mass-1/2 of the particles in the superfluid! Then the fact that polaritons are so absurdly light—10-5 the electron mass—is what makes sound in them so absurdly fast.

• John Baez says:

And by the way, this factor of mass-1/2 is not completely bizarre. If you have a mass at the end of a spring with a given spring constant, it’ll vibrate faster if the mass is smaller, and in fact the period of the oscillation goes like mass-1/2. So we could probably understand all of this in a fairly pedestrian way if we kept working at it a few more days.

• Speed says:

Thanks to all for the comments.

I have a habit of doing sanity checks on numbers and like John I had to look up the speed of sound in air (well, in m/sec — I know about what it is in MPH) and in a well known solid (steel as Todd points out). Then I reviewed the factors that determine the speed and I even looked around for a quotation of speed in a plasma — no joy. So I asked the question.

I also wondered how one achieves such high speeds in a lab environment. Hypersonic wind tunnels (Mach five to 15) and Hot Shot wind tunnels (up to Mach 27) are interesting and complex devices (see Hypersonic wind tunnel for an overview).

My guess is that there is some physics magic involved using magnets or electrical potentials rather than high pressures or explosives. As John said, the particles are, in terms of the world we inhabit, massless. Almost.

8. Giampiero Campa says:

This is another kind of interesting analogy, (sort of the other way around), with a summary here, (but the first article is way better IMO).

I’d be curious to know if people here think that this research has the potential to offer some insight on quantum mechanics. On the other hand, from what i know, the Bohm theory is already on very solid ground and essentially equivalent to QM (not sure if that still holds also when relativity comes into play though), so, in a sense, probably not very groundbreaking …

• John Baez says:

It’s hard to know what to say. Since I’m happy with ordinary quantum mechanics and less happy about Bohm’s theory and other ‘pilot wave’ theories, the idea of using droplets on vibrating water as a model for Bohmian quantum mechanics does not excite me. But to me, the dynamics of those water droplets seems fairly fun to study for its own sake!

Someone who was less happy with ordinary quantum mechanics could easily have a different opinion.

• Eric says:

Out of curiosity, when you say you are happy with quantum mechanics, does that mean you have answered Feynman’s question,”But how can it be like that?” (from Character of Physical Law)? Or have you accepted that it cannot be understood?

It’s difficult for me to conceive of anyone truly being happy with quantum mechanics unless they’ve given up. It doesn’t keep me up at night anymore because I am no longer a scientist, but if I was, the question would haunt me forever.

• John Baez says:

When I say I’m happy with quantum mechanics, I mean several things.

First, I don’t want to ‘explain it away’ by finding some way for it to sit on top of some ‘more classical’ framework, like hidden variables or Bohmian mechanics. I think we need to understand it head-on. That’s why I’m not interested in that water droplet model. Not as a model of quantum mechanics, anyway!

But why don’t I want to ‘explain it away’?

It makes me feel confident we’ll understand quantum theory better when we unify it with our description of spacetime in a theory of quantum gravity. Even better, it gives a bunch of precise clues about how to do this!

A lot of work Urs Schreiber and Jacob Lurie and others have been doing seems to confirm that yes, this idea is on the right track.

Those folks are very smart, so I think it’s best if I work on something else. I feel I contributed a lot at an early stage, but now the puzzle has reached a stage where people who are good at (∞,n)-categories will contribute the most.

So, if I feel haunted at all, it’s just about quitting this particular project before it was done. But I don’t think it needs me, so I should work on something that does.

• Eric says: