Superfluid atoms in a ring.
The title that I gave for this was a new kind of closed circuit,
but I think a better title might be some first steps toward atomtronics.
I want to mention that I’m going to be talking about some recent work in my laboratory
that’s mainly been done by Gretchen Campbell,
and we’re part of the NIST laser cooling and trapping group in the physical measurement laboratory of NIST.
We’re also part of the Joint Quantum Institute that is joined between NIST and the University of Maryland
I can’t resist doing a little bit of shameless advertising.
Especially with so many young people here.
We have lots of opportunities for study and research at the Joint Quantum Institute.
And if you’re at a stage in your career when you’re thinking about where to go next, you might think about us.
And you might end up joining a group like ours or one of the many other groups that are at the Joint Quantum Institute,
studying all sorts of wonderful things about quantum mechanics.
And the other thing I want to say before I really start is: If you see me around, ask me questions!
Because if you ask me a question, I will give you a prize.
So coffee breaks, lunches, dinners, whatever.
If I don’t have something else to do, I’m eager to talk with you.
And this afternoon we’ve got a discussion session.
Tomorrow there’s a master class.
And the next speaker Klaus von Klitzing will be giving you the same prize
which is the 2014 Codata wallet card of the fundamental constants.
Now, at NIST we own the fundamental constants of nature.
And so that’s why I’m giving them out.
And I’m going to give a whole bunch to Klaus, and he’s going to give them out as well.
You heard all about Codata in Ted’s talk, and ok, sometimes Codata gets it wrong but it’s the best we got.
And how can you be a physicist and not have this in your wallet!
Ok, so I want to talk about superfluid atoms in a ring, but I need to give you a little bit of background.
So let’s go a little more than 20 years ago.
It was announced in Science Magazine that the molecule of the year was the Bose-Einstein condensate.
Now, it wasn’t a molecule at all.
And it wasn’t really a new form of matter either.
It’s a gas, for crying out loud, but it’s a really, really cool gas
because it realised a dream that had begun with Einstein 70 years earlier.
When Einstein predicted that, if you had a gas of bosons and you got it cold enough and dense enough,
that something weird and wonderful would happen, namely that there would be a phase transition.
And think about this, this is a phase transition in an ideal gas where phase transitions aren’t supposed to happen.
But because of the quantum statistics of the bosons in this gas, it would undergo a phase transition.
And the nature of the phase transition according to Einstein was that a large fraction of the atoms would stop moving.
Now, remember this is just before the Heisenberg uncertainty principle came along.
So with that we knew that the atoms wouldn’t actually stop moving.
They would just go to the lowest possible state of motion allowed by Heisenberg’s uncertainty principle,
that is by the zero point motion.
So just how cold and how dense would you be.
Well, this isn’t the way Einstein thought about it, but it’s a lovely way to think about it,
based on de Broglie’s idea of matter having a wave-like character.
And so if you have a hot dilute gas, the wavelength of those atoms is short
and the distance between the atoms is long and the wavelength simply doesn’t matter.
But when the gas is dense and cold then the wavelength is long and the distance between the atoms is short.
And you can get to the point where the wavelength is comparable to the distance between the atoms.
And that’s when the magic happens.
And a large fraction of the atoms become a single wave, that is all the atoms having the same wave function,
and they become a single wave that occupies the entire container.
Now, just how cold and how dense do you need to get?
Well, in a typical experiment it might be a few hundred nanokelvin, a few hundred billions of a degree above absolute zero,
with a density on the order of 10^13 atoms per cubic centimetre.
Now, some people think that a density of 10^13 atoms per cubic centimetre is a vacuum,
but the fact is we think this is a really dense gas.
And how do you get that dense?
Well, the first step is laser cooling.
Now, you’ve heard a talk from Dave Wineland and you’ve heard a talk from Ted Hänsch, but neither of them mentioned,
out of modesty of course, that they were the ones who invented laser cooling.
So, along with Dehmelt and Schawlow, a picture of whom you saw in Ted’s talk, these were the inventors of laser cooling.
Each one of these people, by the way, has gotten a Nobel Prize for something else besides laser cooling.
I think that says something about how clever these people are.
But here’s the basic idea: Imagine a gas of atoms and simplify the problem as we always do, as Einstein told us.
Everything should be as simple as possible but no simpler.
And so in the simplification we’ve got a one dimensional gas.
So some of the atoms are heading that way and some of the atoms are heading that way, and you shine in light from both sides
and you tune the light so that it is a little bit below the resonance frequency of the atoms
Now, these atoms moving in this way see the Doppler shift of this laser beam
as putting its frequency closer to the resonance frequency of the atom.
So these atoms preferentially absorb from this laser beam and slow down.
These atoms, on the other hand, see these laser beams as being the ones that have the right frequency to be absorbed.
And so this atom preferentially absorbs from this laser beam and slows down.
Now, you can generalise this to three dimensions and have laser beams coming in backwards and forwards and up and down.
And now the atom, no matter which way it moves,
sees the laser beams that oppose its motion as being the ones that are closer to resonance and it will slow down.
And this was first realised in the laboratory by Steve Chu.
You don’t need these pictures but just to remind you of what Dave Wineland and Ted Hänsch look like.
If you want to ask them about laser cooling.
And if you find Steve Chu you can ask him as well.
But one of the things I want to point out is that one of the reasons why these characters got the Nobel Prize
for laser cooling was that laser cooling worked even better than those original researchers thought.
In fact, we eventually got 100 times colder, over 100 times colder than we were supposed to get using laser cooling.
And I’m not going to tell you that story.
It’s a wonderful story but we can talk about it later.
But even that wasn’t cold enough or dense enough to achieve Bose-Einstein condensation.
So what could you do?
The answer was rather simple.
Evaporative cooling.
You know that when you blow on your coffee to make it cold, what’s happening is that you are allowing
the most energetic of the water molecules to escape from the surface, and what is left behind is colder.
Well, we do exactly the same thing by trapping our atoms in a magnetic trap or a laser trap,
allowing the most energetic atoms to escape, and what’s left behind is colder.
And using evaporative cooling in the early days in a magnetic trap, what I call the heroes of Bose-Einstein condensation,
were able to reach temperatures colder than was possible by laser cooling, down into the nanokelvin regime,
and were able to realise Einstein’s strange and wonderful prediction.
So, who were these heroes?
Well, one of them is Dan Kleppner who is often called the godfather of Bose-Einstein Condensation.
I’m glad to see you recognised that logo from the movie.
And the reason he’s called the godfather is because he taught us about the techniques that were needed to make Bose condensation.
But these were the ones, the heroes who actually achieved it: Eric Cornell and Carl Wieman at Boulder.
Wolfgang Ketterle at MIT.
And what we’re looking at here is a velocity distribution of a gas of atoms
as it’s cooled from a temperature of 400 nanokelvin, too hot for this phase transition to occur.
And so you see this broad featureless distribution as you would in any thermal gas.
And then when the temperature goes down to 200 nanokelvin you get this huge peak of atoms around zero velocity.
And that’s the condensate.
That got these guys the 2001 Nobel Prize in physics.
Carl Wieman is supposed to be here.
I haven’t seen him yet either.
But if you see him ask him about this.
So what is a Bose-Einstein condensate?
It’s a macroscopic quantum state.
It’s thousands to millions, sometimes even billions of atoms all in the same state.
It is laser-like in its coherence in the wave nature of these atoms.
So, just as a laser has many, many photons in the same state a Bose-Einstein condensate has many, many atoms in the same state.
And very often it’s big, hundreds of micrometres across, or even larger, like a millimetre.
You young people can see something that small. I can’t.
But if you can see it with the naked eye, it’s macroscopic.
Ok, so what do we do?
We put this gas which, did I mention it’s superfluid.
No it doesn’t have that. Oh it is, yes ok. I did mention it – here.
This is a superfluid.
So, this is a new kind of superfluid.
We’ve had liquid helium. Superfluid helium.
We’ve had super conductors which are a superfluid, electric superfluid.
And now we have a gaseous superfluid.
And what we do is we put it into a ring.
Now, it turns out that if you have a laser beam tuned red of the resonant frequency of an atomic transition
then the atoms will be attracted to the most intense part of that laser beam.
So, what we do is we focus down a ring of laser light.
So, that it’s focused down to a ring that’s about 50 microns in diameter.
And then we focus using a cylindrical lens.
We focus another laser beam down to make a sheet of light.
And the inner section of this ring of light and this sheet of light makes a torus in which we can trap our atoms.
And we can get a persistent current of atoms going around this ring that lasts for as long as the atoms do.
The only thing that stops this persistence of current is the fact that we have an imperfect vacuum.
And eventually the atoms are scattered out of this ring by the room temperature residual atoms.
Mostly hydrogen that are inside our imperfect vacuum.
And you might say, well, why don’t you make your vacuum better?
We made it as good as we could.
And that’s what we get.
But 60 seconds, in our business 60 seconds is forever.
So this is fantastic.
So, now I want to emphasise that this is the work of Gretchen Campbell.
And, of course, we call the group that works on this “The Fellowship of The Ring”,
and you can see the former and current members as well as our theory collaborators.
Here’s a group picture of Gretchen.
So, there’s Gretchen leading the fellowship.
And here you know you have the graduate students and the postdocs.
And the theorists.
And, of course, there are people all over the world doing wonderful experiments using rings.
And these are some of them, and probably I forgot some.
And I’ll be very grateful if you tell me if I did.
But then what’s the next thing?
Now, we’ve got a ring and this is the simplest circuit you can imagine.
It’s the atom equivalent of a loop of wire, but we want to do something more interesting.
And if I had a superconducting circuit what would I do with that superconducting circuit?
I would put a Josephson junction in it.
And the way we make a Josephson junction is we shine in a beam of light on one end of this ring
and that beam of light is now tuned to the blue, that is to the high frequency side of the atomic resonance.
This kind of a laser beam repels the atoms.
And so you see that there’s a depletion in the atom number here.
And the atoms have to go up over this barrier to go around the ring.
So, this creates a weak link or a Josephson junction.
And I want to emphasise that, well, if you’ve studied the Josephson effect and Josephson junctions,
you may have been thinking of the kind of Josephson junction
where you have a very thin layer of dielectric and the electron pairs tunnel through that dielectric.
And that is indeed a kind of Josephson junction, the sort of ideal sort of Josephson junction,
that I think that Brian Josephson – who is sitting right here, isn’t this fantastic? – was thinking about
when he came up with this.
Now, you young people, by the way, Josephson, how old were you, 20?
No probably 22.
22, ok, I don’t think that many of you people are that young.
And Brian came up with something that changed our whole way of thinking about superconductors
and the possibility of making superconducting circuits.
So, how is that for a challenge for you young people?
Anyway, the point is, so you know, seek out Brian Josephson,
the point is that that’s not the only way of making a Josephson junction.
And even in superconductors there are things called Dayem bridges which are a kind of Josephson junction
where you’ve just thinned out the superconductor here.
And that’s what we’ve done in our Josephson junction.
You can see that the superfluid atomic density, it’s almost all superfluid, has been thinned out there.
Ok, that’s how we make a Josephson junction.
How do we control the current?
The way we control the current is by taking that Josephson junction and rotating it around the ring.
Now, why is this a good thing?
Well, if we were in a reference frame that is rotating with the junction
then we would see a Coriolis force in that rotating frame, in addition to the centrifugal force,
but the important thing here is the Coriolis force.
That Coriolis force is a term in omega xv, the rotation vector crossed into the velocity.
Well, the Lorentz force on a charge particle in a magnetic field is vxB.
So it’s got the same functional form.
So, it turns out that going into a rotating frame for neutral atoms is just like applying a magnetic field
for charged electrons that you would have in a superconducting ring.
And so you have an analogy.
Now, what happens when you apply a magnetic field to a ring of superconductor that has a Josephson junction in it.
The current in the ring increases so as to shield out the magnetic flux,
until you reach the critical current for the Josephson junction and then it allows a flux quantum in.
We expect exactly the same sort of thing to happen here.
In the rotating frame as you rotate more, which is equivalent to more magnetic field, you get more current,
obviously because in the rotating frame you see the atoms passing through the junction in the opposite direction.
So there’s an increase current the faster you rotate.
But at some point you reach the critical current that is allowed to go through the junction
and then it will allow in a quantum not of magnetic flux, but a quantum of circulation.
And then we will look at the ring to see whether it’s rotating.
How do we tell it’s rotating?
We release it and after a time of flight.
If it’s not rotating, the hole that was in the middle of the ring fills in.
But if it’s rotating, the hole can’t fill in and we see this, we see a hole in the centre of the cloud because, of course,
if it has angle momentum the atoms can’t be at the centre.
And just by looking at the size of the hole, we can tell what the circulation is, and the circulation is quantised
because this is a single wave function, and the phase of the wave function going around here
which tells you what the gradient of that phase, tells you the velocity, that has to integrate up to a multiple of 2 pi.
And so we can have 1 unit of circulation, 2 or 3 or as many as we want
and we can tell just by looking at the hole how many we have.
So here’s the results of one of those experiments.
Here what we did was we rotated the barrier around the ring at different velocities.
And when we did it at low velocities and then turned it off and looked at the released condensate we saw no circulation.
But when we did it at a high velocity then we always got circulation.
And somewhere in between there was a transition.
And that was for a barrier of a certain height.
When the barrier was just a little bit higher that transition occurred earlier.
Just as you would expect.
You would expect that when the barrier is higher the critical velocity is lower,
the velocity that you would need to flow in order to break the superfluidity and get an excitation.
So, we developed a toy model of that excitation that involved creating some vortexes here
and then the vortexes repel each other and head to the outside.
And that toy model seemed to agree reasonably well with theory.
And the toy model agreed with experiment.
But it didn’t agree at all with making the critical velocity the speed of sound.
And this was a clue to the idea that it wasn’t phonons that were the excitations
that were arising when we exceed the critical velocity.
But instead it was something like vortexes.
Now, I want to emphasise that this isn’t the first time someone has done this kind of an experiment with a fluid.
Richard Packard and his group at Berkeley have used superfluid,
both Helium 3 and Helium 4 to make this kind of a device and sensitive enough to detect the earth’s rotation.
We’re doing the same thing but with a gas.
Now, we’re not as good as they are yet.
We’re not detecting the earth’s rotation but we are doing some interesting things and having some fun.
So, let me tell you about one of the fun things that we’re doing with these superfluid gases.
Hysteresis, why is there hysteresis in this system?
Well, remember the story that I told you about rotating the barrier around the ring.
So, in the rotating frame you see flow in the opposite direction at about the velocity that the barrier is rotating
until you finally reach that velocity that’s high enough that it will create an excitation.
That is it’s no longer superfluid, it creates an excitation, and that excitation brings into the ring a quantum of circulation.
So, now all of the fluid in the ring is circulating around like that with some velocity.
Now, let’s say that the critical velocity, just for the sake of argument,
imagine that the critical velocity was almost as big as the velocity when you had a quantum of circulation in here.
By the way, that velocity for a 50 micron ring is about 1 turn per second.
So it’s a really quite manageable velocity.
You could almost do it by twiddling the mirror mounts by hand but we in fact use a spatial light modulator to do it.
But the point is that once you allow a vortex to go through here and come into the inside, so that you now have circulation
around here, that circulation is almost at the same velocity at which the barrier is rotating around.
So that means the relative velocity between the barrier and the fluid is nearly zero.
If you’re going to go back and make the flow stop, you’re going to have to make the relative velocity
between the barrier and the fluid be large, close to the velocity of one unit of circulation.
And so you expect to have a different result coming back down as you did going up which is what we call hysteresis.
So here are a number of transition curves for different barrier heights.
So this is the lowest barrier and this is the higher barriers.
Now, I want to emphasise these are not tunnelling barriers
in the way that Brian Josephson originally imagined the Josephson effect.
The height of these barriers is lower than the energy of the atoms.
So what is happening is the atoms are just going over the barrier classically but as a result of the barrier being there
the superfluid density is lower and that’s all that’s needed in order to see the kinds of effects that we’re interested in.
So here with a low barrier you have to go to a high enough velocity and then you see this transition to a state of rotation.
And when the barrier is lower you make that transition at a lower velocity.
Now, what happens when we go back the other way?
So going back the other way you see you have to go until you’re at a quite low velocity because the fluid is already circulating.
And you make the barrier rotate at a much lower velocity,
and then finally when the relative velocity is big enough you make the transition.
And when the barrier is higher you don’t have to make that relative velocity as big and it occurs at a higher velocity.
And now, if we put the two curves together,
you see you have this classic hysteresis loop that you expect to see in so many kinds of systems.
And here we’ve seen it in this superfluid atomic gas.
So hysteretic behaviour is central to a lot of electronic devices and processes,
things like memory and noise tolerant switching, like Schmitt triggers, that you may be familiar with from electronic design,
and now we’ve added that feature of hysteresis to our tool box for superfluid gases.
So let me just come to a close by showing pictures of the people who were part of the team who have recently done these things.
There’s Gretchen, the leader of this team.
We’ve been very happy to have the collaboration of Chris Lobb who is a real SQuID guy, that is electronic SQuIDs, and Avinash
and Steve and Fred and Erin have all been part of that.
And the more recent team has added a few more young people and they’re doing wonderful things right now.
So, besides the things I’ve told you,
by using interference we can actually see interference fringes between a non-rotating gas and a rotating gas.
And this is something you’re never going to do with a liquid or with a superconductor.
We can visually see these interference fringes and measure the phase around the ring.
Gretchen and her team are making DC SQuIDs, that is things that have two junctions.
They’re generating sound waves by modulating the Josephson junction to create sound waves going around this ring,
studying thermal effects, other things I didn’t even put on here
were watching a standing wave of sound being dragged around the ring by the superfluid rotation.
So this is the end of my talk, but it’s certainly not the end of this research.
We’re doing such incredibly exciting things, but I want to remind you, ask me questions, because you want to get this card.
And let me tell you why.
And Klaus von Klitzing is going to tell you more about this.
This is the last card on which Planck’s constant will have any uncertainty.
The next time this card comes out Planck’s constant will be exact.
And so will the charge on the electron.
And so will the Boltzmann constant.
And so will Avogadro’s number.
And Klaus von Klitzing will tell you why.
Thanks very much.