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.

LA's big lake of colloids

The New York Times is running a piece about tap water and the regulation thereof called "That Tap Water Is Legal but May Be Unhealthy". One particular contaminant becomes dangerous on exposure to sunlight so, at a lake in Los Angeles, they've tipped 400,000 plastic balls into the lake to block out the sunlight.

Perhaps this shows I've been in stat-mech too long. All I could think about upon seeing this picture was - "cool, a massive 2D elastic disc simulation!".

It's quite interesting where the crystal structure is interrupted - each one of those interfaces costs a lot of free energy. You can also see it's not truly 2D as along certain stress lines the particles have gone up and over to reduce the energy.

I wonder if it's in equilibrium or whether it'll age with time...

This is what science can do to you :-s

Don't know what fair use would be for stealing this photo but hopefully if I link to the NYT enough they won't mind - go and click on one of their ads of something...

Backup news

Anyone that's been here from the start will know I have a slightly unhealthy obsession with backups.  A couple of things have changed since I last blogged about this.

Time Machine
Firstly, I now have a mac at home and I've started using Time Machine. I don't want to pat Apple on the back too much because that really gets of my nerves, but Time Machine is absolutely fantastic.

It's exactly how personal backup software should work. You buy an external hard disk, tell Time Machine to backup there, and then you're done. You never need to worry about it again. Most of the time when I need my backup it's because I've accidentally deleted something I shouldn't. Time Machine allows you to, as the name suggests, just go back in time and find it before you made the mistake. Works like a dream.

After a botched attempt to upgrade to Snow Leopard I recently had my first call to do a complete system restore. All I can say is that it seemed to work perfectly for me - it didn't even take that long.


Rsync + windows
At work we backup to an external file server. Until recently that was Linux based and so I had no trouble using Rsync. Now we've been moved to a Windows server which creates all kinds of problems. Rsync just doesn't get on with Windows. Anyway, after a bit of poking around I finally have a script that does the job. This is my basic rsync call now:

rsync -rptgoDhpP --modify-window=1 --delete --log-file=RSYNCLOG --exclude-from=./exclude /home/username/ username

I'm pretty sure most of those options could be replaced with the -a but honestly, now it's working I don't want to touch it! The key command is the modify-window. This accounts for the different way that Windows and Unix file systems time stamp modified files.

SVN - Subversion
For programming and writing papers (in LaTeX) I've started using subversion to take care of version control. I'm also using a shared repository to co-write a paper at the moment - it handles simultaneous editing quite well. There is a start up cost in getting your head around how it works, I found this page very helpful, but once you're there it works very nicely.

I mention it here because the version control works a bit like a backup. You can step back through committed versions very easily. If you use OS X then it's installed along with XCode so you probably have it. With Linux it'll be in the standard repositories.

Well that's enough backup geekery for this year. Anyone using anything that they're particularly happy with? I've kind of given up on backing up over the internet for now but would be interested if there's been any developments.

An unintuitive probability problem

Probability can do strange things to your mind. This week I had a probability problem where every time I tried to use intuition to solve it I ended up going completely wrong. I thought I'd share it as I think it's interesting.

Consider a one dimensional random walk. At each time step my walker will go left with probability , and right with probability . It stays where it is with probability . Furthermore these probabilities are dependent on the walker's position in space, so it's really and . I'm imagining I'm on a finite line of length, L, although it doesn't matter too much.

Now if , then we just have a normal random walker. In my problem I have the following setup: but . What does this mean? At any given point, x, my walker is more likely to go left than right. If it does go left it will come back with the same rate (although it's more likely to go left again).




So here's the question: If I leave this for a really long time, what is the equilibrium probability distribution for the walkers position, ?

Great LHC animation

The purpose of this blog was to showcase other types of physics other than the LHC. But I can't resist, this is a really nice animated video showing the stages of getting stationary protons up to 7TeV

http://cdsweb.cern.ch/record/1125472

(via @CERN)

Speed limit for computer processors - serial vs parallel

This news item from Nature about this PRL talks about how computer processors are going to hit a speed limit due to the speed at which a system can make transitions between quantum states.

There are two independent bounds on this minimum time — one based on the average energy of the quantum system, the other based on the uncertainty in the system's energy. In their calculations, Levitin and Toffoli unify the bounds and show there is an absolute limit to the number of operations that can be achieved per second by a computer system of a given energy.

I'm not an expert in quantum information so all I can say is that it looks interesting. There are implications for myself because most of my work is pretty intensive computer simulation. Some of what I do simply needs fast processors, there are sections of my Monte Carlo simulations that cannot be parallelised (fancy cluster algorithms being one). So for these, in principle, it limits what could ever be done.

However, mostly my limit is on what statistics I can collect and that can be solved by using more and more processors. The move from single core being standard, to eight these days, has been a revolution in terms of what I can now get done in a reasonable time scale.

In fact one very interesting development is using standard computer graphics cards to perform molecular dynamics (MD) simulations. I've only read the abstract of this paper I'm afraid but they've apparently done this. Graphics cards designed for games have many little processors on them (GPUs) and they can all work on the problem more efficiently than one super powered CPU trying to do it on its own.

So next time you say that computer games are a waste of time think of this...

There's more to the LHC than bloody black holes

The LHC is cold again. This is very exciting, and also it can't come soon enough. In the absence of any actual science going on an endless stream of bollocks seems to have been coming out about the collider. The latest being this drivel about things coming from the future to... oh God I can't be bothered. It rather upsets me that the only things people really know about the LHC are that it might make a black hole and maybe something is coming through time to sabotage it. So I thought I'd talk about why this machine is ridiculously fantastic and complicated (the more likely cause of breakage).

One of the features of synchrotrons that I've always thought is amazing is the way they cool the beams. By cool I'm not talking about temperature around the beam pipe (although that's bloody cold too so that the magnets work). I'll quickly describe what it is and how people solve it, although I'm still not 100% sure how they've solved it at the LHC.

Our general collider accelerates particles around a ring using strong electric fields. The particles are bent into a circle by bending magnets and they are kept in a beam by the focussing quadropole magnets. The effect of these magnets is that if a particle is heading sideways out of the beam then they push it back in in the opposite direction. In this way the particles kind of snake around the course never straying too far out of line. The task of cooling the beam is to reduce this snaking as much as possible so that we have a really dense, straight running beam.