Even colder still

In a previous post I was talking about how you can use a laser to cool atoms. By tuning the laser to just below the energy of an atomic transition you can selectively kick atoms that are moving towards the laser. If you fire six lasers in (one for each side of the cube) you can selectively kick any atom that is trying to leave the centre. So we've made a trap!

There is a hitch unfortunately. There is a minimum to which one can cool the atoms, once the atoms have an energy that is comparable to the photons coming from the laser then that's about as low as they can go. After all, there's only so much you can cool something by kicking it. We're already pretty cold - around 100 micro Kelvin - we'd like to go a bit colder if we can. Now we're into magnetic traps.

Magnetic Traps

Up to now we've been acting quite aggressively towards the atoms - kicking anything that's moving too quickly. To do better we're going try and round them up where we can control things better. Fortunately there's a neat way to do this. We can make use of an inhomogeneous magnetic field and the Zeeman effect.

If you apply a magnetic field to our gas of atoms then the magnetic dipoles of the atoms tend to line up with the field. Being quantum physics they can only do so in a discrete number of ways. What happens is that the transition that used to be a line splits and shifts into a number of different lines.

If we use a stronger field then the shift is larger. We can finely tune the energy at which our laser will interact with the atoms. So now we do this; if we put a magnetic field that is zero in the middle of the trap and gets bigger as you move away from the centre (you can do this) then we can control how hard we kick the atoms depending where they are. If we do it right then inside the trap we hardly kick them at all and outside trap we kick them back in.

Evaporation

We've managed to confine the atoms in our trap, the final step is to switch off the lasers (to stop all that noisy kicking and recoiling) and to try and use evaporation to get rid of as much energy as possible. It is understandably quite complicated to stop them all flying out once you've switched off the lasers and unfortunately it's at this point I start getting lost! The actual cooling mechanism is nothing more complicated than why your cup of tea goes cold.

After all this we're down the micro Kelvin level - a millionth of a degree above absolute zero! At these sort of temperatures the atoms can undergo a quantum phase transition and become a Bose-Einstein Condensate (BEC). This is a new state of matter, predicted by theory and finally observed in the nineties. As far as I know this is as cold as it gets anywhere in the universe.

Well I think I'm done with cooling things now. It starts off beautifully simple and then gets a bit harder! Needless to say I salute anyone that can actually do this - it's back to simulations for me.

EDIT: I over-link to wikipedia but this is a good page on Magneto-optical traps

Ghost Jams

via Lester, a nice video showing ghost jams in action



See New Scientist for more.

The drivers were asked to drive around at a constant speed. For a while this works OK, eventually a ghost jam develops and propagates at the same speed that they're observed in real traffic. I don't know if they tried to apply any external stimulus to see if they could guide it better.

Simulating a molecule with a quantum computer

Simulating a molecule

There's a fairly nifty paper out in PRL on simulating a molecule with a quantum computer. In principle doing calculations on quantum systems will be much faster with quantum computers (when they become a reality) thanks to being able to hold the computer in a superposition of states. These guys have had a bash using an NMR based "computer" - it's pretty fun.

Help with twitter name

What do you think this blog's twitter feed should be called?

KineticallyConstrained is a bit long (will hurt the retweets)
KineticCon?
KConstrained?
Kinetically?
KinCon (taken)
TwittersPointlessDontBother?

So many important decisions...

Do you like my new header?

OK, so I'm no Banksy, but I do like green. I'll probably be playing around with themes a bit over the next few weeks.

Hopefully the header captures how "kinetically constrained" can apply to complex statistical systems and that sort of stuck feeling that I can never quite shake off. Look at me full of bollocks, maybe I can get on Newsnight review or something.

How should we teach Maths

I came across this new feature in the NYT via Science Blogs by Steven Strogatz. You may remember him from his paper with Duncan Watts on small-worlds that arguably kick started modern network theory. It looks like it's going to be a regular series so I highly recommend adding the feed to your rss reader.

The article that first caught my eye was called Rock Groups. It starts by differentiating between the serious side of arithmetic and the playful side. This is something I've long gone on about but never quite had the nice way of putting it like these guys do. Maths teaching for kids is like torture. I was having a discussion a while ago where I questioned whether we really needed to recite endless times tables aged 10 years old. A suggestion that drew scorn from my opposite number. But really, why?

The book that is heavily quoted in the article, "A Mathematician's Lament" by Paul Lockhart. It starts with a musician having a nightmare that children are not allowed to touch an instrument until they have mastered the theory of music and how to read a score. Only after many painful years are they allowed to lay their hands on an instrument.

This is a powerful analogy. You don't have to learn all the nuts and bolts of mathematics before you can start playing with numbers. Back in the Strogatz article he shows how much you can discover without being able to do any addition at all, just by grouping rocks. I wish I could quickly multiply two large numbers in my head but it wouldn't make me a better mathematician. It's like arguing that the best playwright should be able to spell every word in the dictionary.

The beautiful thing about the rocks is that it shows how much you can learn about number by pushing things around with your hands and being creative. Perhaps all those people who complain to me that "oo I could never do maths me" would have enjoyed it more if it was based on this rather than being expected to master "a complex set of algorithms for manipulating Hindi symbols".

Make sure you keep up with the Strogatz series. I found a pdf of the essay that inspired the Lockhart book. If I ever get through my Christmas backlog I might get around the getting the book.

Laser Cooling

Last semester I was helping out teaching a bit of quantum and atomic physics. It was quite fun going back to stuff I was a little hazy on the first time. I finally understand the periodic table for one thing. Another thing that I knew about but never really got the detail is laser cooling. This is really nice, I'll blast through it here. Watch out for the stat-mech bit, blink and you miss it.

In an atom electrons are not free to sit anywhere they want (more or less), they inhabit precisely defined quantum states that have well defined energies, angular momenta etc. Therefore if you give an atom a kick then it will release the energy you give it in precisely defined packets of energy. So if you take the light emitted by the atoms and put it through a spectrometer (could just be a prism) you'd see something like this, from here, for sodium.

You'll recognise the orange line from the street lamps that are slowly on their way out. I did a version of this experiment when I was an undergrad where we did the opposite, we shone white light through sodium gas and while most of it goes through the frequencies that match the right transition frequencies get absorbed and are missing from the final spectrum. Might look like this, ish

Notice that the lines aren't all that sharp whereas I said they should be precise lines. This is for a number of reasons. One is that the uncertainty principle doesn't like precise energies. There's an uncertainty attached to the lifetime of atomic transitions or collisions. Another, more important effect is Doppler shifting due to the temperature of the gas. We can assume that the atoms in the gas have a distribution of velocities that comes from the famous Boltzmann distribution

Light emitted from a moving atom will be Doppler shifted which will take our precise emission line and spread it out around the average. This property turns out to be very useful and what we'll use. First a mention about the laser.

Lasers are brilliant. With a laser you can send in a beam of photons with a highly tuned narrow band frequency. When a photon hits with a frequency that matches the absorption frequency of the atom, they collide and scatter. When it's too much or too little it will most likely just go straight through.

So finally we get to how you cool the gas. If you send in a laser pulse into a warm gas of atoms then different atoms will see different things. Thanks to the Doppler shift, an atom moving with speed, v, will see the laser frequency, f_0, Doppler shifted to (c = speed of light)

Atoms moving away from the laser see it red shifted (lower frequency), atoms moving toward the laser see it blue shifted (higher frequency). If we tune the laser to just below the absorption frequency of the atom then the only atoms that collide with the beam are those moving towards it (the ones that see the blue shift).

Were it not for the precision of the transition level the laser would equally kick atoms moving towards it and atoms moving away - adding no net energy into the system. However, if we only collide with atoms moving towards the beam then we can actually remove energy. What's even more staggering is that this actually works!

Laser cooling can make things seriously cold. You may have seen the headlines that the LHC is colder than space. Impressive given the size of the thing, but space is about 2 Kelvin. This is peanuts compared to laser cooling. This can get a gas down around 1 mK - that's a factor of a thousand. You can get even colder with new techniques but somehow laser cooling pleases me the most.

So that's laser cooling. It's beautifully simple, uses basic ideas from quantum mechanics, relativity, statistical mechanics and then makes something brilliant thanks to a laser.