Cold Atom Tools

Keeping BEC Cold

drorzel — Wed, 04 Dec 2013 08:59:18 +0000

Keeping BEC Cold

I know I said there weren't going to be physics posts for a while, but yesterday our Communications office passed along a media request about this paper on feedback cooling of BEC, from some sort of communications-person mailing list. I'd seen it talked up elsewhere-- here, for example, so I banged out an email to the reporter in question. Who didn't use any of my stuff in the story that ran late last night.

Having put in the work, though, I may as well get something out of it, so here's the email I sent. Questions in bold are from the original request. The paper is in the New Journal of Physics, which is an open access journal, if you want to read it. I'd add figures and links to old posts and that sort of thing, but I've already spent longer on this than I should've, so you just get the email straight.

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Questions for the sources include: 1) What is the importance of this finding regarding the "coldest" material in the universe?

One of the main applications people talk about for ultracold atoms is in the area of precision measurement, using the quantum nature of the atoms to make extremely sensitive detectors of acceleration, rotation, gravitational forces, and magnetic fields. These can be useful both for fundamental physics studies--looking at tiny interactions in fine detail-- and for more practical projects. When I was a post-doc, the lab I worked in got funding from the Navy to develop atom-based detectors of rotation and gravity gradients because they might be useful in submarine navigation. A sensitive rotation detector can tell you how you've changed the orientation of the submarine, and a gravity sensor could help detect underwater mountains and other obstacles, in both cases without needing to send out sonar pulses that other people could detect.

These sorts of detectors mostly work by using the wave nature of matter, taking a bunch of atoms and splitting them apart onto two different paths, then bringing them back together recombining them. Differences in the interactions experienced by the part of the atoms that went along one path versus the other show up as changes of the final state when you recombine them. People do the same thing with light waves all the time-- the best current sensors for a lot of these things involve light-- but atoms offer a couple of advantages having to do with the fact that they're massive particles, and thus interact much more strongly with gravity.

For this to work really well, you need the best possible source of atom waves-- a collection of atoms that behave basically like a laser, with all of them having the same wavelength and "phase," meaning that they're all in step, with the peaks and valleys in the same places. Ultra-cold atoms from a Bose-Einstein Condensate are, in principle, a great way to do this-- a BEC is, loosely speaking, a large collection of atoms all occupying a single quantum state, so all of the atom waves are perfectly in step. The practical problem with this is that a BEC is a fragile thing, so cold that a single atom absorbing a single photon can significantly heat the sample, which disturbs the waves, and thus reduces the sensitivity. But you need to shine light on the atoms to know what they're doing, which means you always have a bit of heating going on. This limits the length of time you can keep a BEC around as a useful source of cold atom waves.

The new study is a theoretical investigation of a way to fix this problem. Having light shining on the atoms to monitor them will give you some heating, but if you're clever about it, you can use the information you get about what they're doing to correct for that heating-- making small tweaks to the light and magnetic fields used to confine the atoms that takes that heat out. This kind of feedback system allows you to adjust the parameters in a way that can extend the useful lifetime of a BEC dramatically.

Some previous simulations had suggested that this might be possible, but this is a very tricky problem to solve, and the methods the previous studies used relied on some approximations to simplify the problem to something they could actually work with. That always leaves open the possibility that you've approximated away the killer problem that will prevent the system from working the way you'd like. This new paper uses a different approximation, that captures more of the details of the interaction, and while it shows the limits of the previous work, it also suggests that the feedback scheme could work in a practical system.

2) How cold is cold in this instance?

That's a harder question to answer than you might think. There are two different ways to talk about temperature in physics: one is in terms of the speed at which the atoms in your sample are moving, and the other is in terms of the number of quantum states that they occupy.

In speed terms, you can never totally get rid of the motion of the atoms. If you let the sample go, turning off the trap that confines them, you'll see them fly away at some speed, that probably corresponds to a billionth of a degree (Celsius) above absolute zero.

In occupied-state terms, the sample is essentially all in a single one of the possible energy states an atom can have inside the trap that holds them. There's a tiny residue of atoms in higher-energy states, which corresponds to a really tiny temperature. Again, this is probably something in the nanokelvin (billionth of a degree) sort of range.

Those values are purely practical limits-- you can never remove all of the energy from the system, because it would require an infinitely long time to get all the energy out. You can get as close to zero energy as you have the patience to wait for, though. The numbers they use in their simulation (and that people reach in experiment) are a sort of compromise--they could get colder, but it's not worth the extra time.

Probably the best thing to say about the temperature is that it's as close to absolute zero as you'd like it to be.

(Though, again, this is a theory paper, so their atoms are simulated in a computer. The numbers they put in are based on real experiments, though.)

3) What is the next step in the research?

This is a theoretical study, using a computer to simulate the behavior of atoms in a BEC exposed to their particular feedback scheme. The next step is to actually do it with real atoms in a real trapped BEC.

This shouldn't be too hard to arrange, as they propose two different ways of realizing the feedback, closely based on two different systems people use for studying BEC. There are several different experimental research groups that could potentially implement this sort of scheme, scattered all around the world, including in Australia where some of these people are based. It's a good bet that they've been talking to experimenters about how to do this, and there are almost certainly groups tooling up to implement this right now (if they're not already well into the experiments).

Once they show it can work to keep the BEC around and coherent for a long time, then it's a matter of integrating this with the various precision-measurement systems. Again, there are a lot of people who do this sort of thing, and I'm sure they're watching this very closely.

drorzel Wed, 12/04/2013 - 03:59

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When Is a Composite Object a Particle?

drorzel — Tue, 15 Oct 2013 08:24:06 +0000

When Is a Composite Object a Particle?

Through some kind of weird synchronicity, the title question came up twice yesterday, once in a comment to my TED@NYC talk post, and the second time on Twitter, in a conversation with a person whose account is protected, thus rendering it un-link-able. Trust me.

The question is one of those things that you don't necessarily think about right off-- of course an atom is a particle!-- but once it gets brought up, you realize it's a little subtle. Because, after all, while electrons and photons are fundamental particles, with no internal structure, atoms are made of smaller things. But somehow we get away with thinking of them like single particles when talking about things like cooling clouds of atoms to BEC. We trest rubidium atoms as bosons, even though they're really collections of a hundred-odd fermions, and we talk about them having a single de Broglie wavelength despite being a big assemblage of other stuff. But it clearly works, as nearly 20 years of BEC experiments demonstrate. So how do we get away with that?

I had never really thought of this question before Eric Cornell brought it up in a talk at a conference-- I think it was a Gordon Conference, but I'm not sure-- and happily, he explained it very nicely. The rule of thumb is that you can safely describe something as a single particle as long as the energy of the particle and the stuff it interacts with is smaller than the binding energy of its component particles.

"Binding energy" is a term of art that means, roughly speaking, "the energy you would need to put in to pull a piece out." If you pick a random atom, the binding energy of its most loosely bound electron is probably around 10 eV worth of energy, or 0.0000000000000000016 joules. That's the gravitational potential energy of a 1-gram mass lifted up about the diameter of an atomic nucleus, or a baseball with a velocity of a few nanometers per second. But it's a huge amount of energy to pack into the space of a single atom, enough to rip the atom apart.

So as long as you're dealing with particles having less energy than that, you can safely treat atoms as single particles, albeit with some internal energy states. A single photon with energy less than the ionization potential-- basically anything with a wavelength longer than a couple hundred nanometers, in the deep UV range-- might move an electron from one state to another inside the atom, but that doesn't change the single-particle nature of the atom any more than flipping an electron from spin-up to spin-down changes it. And as long as the kinetic energy of the atoms in your sample is less than that, collisions between atoms aren't going to break them apart, so you can think of them as single quantum particles.

How much kinetic energy do atoms have? Well, the temperature of a sample is, in the simplest description, a measure of the average kinetic energy of the particles, with the conversion from temperature to energy given by Boltzmann's constant k_B which is 1.381x10^-23 joules per kelvin (fun fact: this is the one major constant I have trouble remembering. I know the digits, but regularly screw up the exponent, for some reason, including at least once when writing a homework assignment...). That's maybe not the most illuminating number, but there's a convenient rough conversion that AMO physicists like me tend to know, which is that room temperature is about 1/40th of an eV. That's room temperature in Kelvin, mind, so to get the thermal energy up to the point where you have to really worry about the component particles of atoms, you would need 400 times 300K, or 120,000K. So as long as you're not working on the Sun, it's probably safe to consider atoms as single particles.

(Now, there are lots of scenarios where other factors complicate this-- I got my Ph.D. studying ionizing collisions in metastable xenon, where the atoms were placed in an internal state with a lot of energy, so two atoms together had the energy needed to ionize one. Other experiments use things like two-photon ionization, where a single photon doesn't have enough energy to blast an electron out of an atom, but two of them arriving at the same time do. In those situations, you need to worry a bit about the details of the internal structure, but in a pretty minimal way.)

The energy scale involved changes for different situations, but the arguments remain essentially the same. Atomic physicists essentially always treat the nucleus of an atom as a single particle, despite the fact that it's made up of protons and neutrons, because the binding energy involved is vastly greater than any energy we deal with. You need energies thousands to millions of times greater than the ionization energy to break a nucleus apart, so for our purposes, it's a particle. Again, a particle with some internal states-- you can flip nuclear spins and that sort of thing-- but a single lump of stuff with a mass and spin determined by the sum of all its components.

In the other direction, many molecules have binding energies lower than those of atoms, so the energy needed to rip an atom out tends to be less than the energy needed to rip an electron out of a free atom. But it's not a huge difference-- the energy involved tends to be on the several-eV sort of scale still, so well into the ultraviolet. That is what makes UV light somewhat dangerous, though-- the photons have an energy that's high enough to break some organic molecules apart, and damage living organisms as a result. Thermal energy continues to not be an issue, though.

This is why Markus Arndt's group in Vienna is able to do amazing experiments with interference of large molecules, including seeing diffraction patterns with 430-atom organic molecules and using single-molecule detection to watch the diffraction pattern build up (the "featured image" up top is from this page, and is a version of the data featured in that second paper). Even though their molecules are evaporated from an oven at (probably)500-600K (they don't cite a temperature, but point at this paper), the energy of the individual molecules is low enough that they can really be thought of as single particles. These are particles with huge numbers of internal states-- they talk about "1000 degrees of freedom" in promoting the paper-- but that doesn't prevent them from showing wave behavior. Each molecule interferes with itself, and as long as you can keep changes in the internal state from producing a large shift in the pattern, you can still build up a terrific interference pattern. These are just awesome experiments, by the way.

(Full disclosure: I met Arndt at a conference in Europe back in 2001, and he was very helpful when I contacted him to get permission to reprint one of his graphics in my first book, suggesting a better graph than the one I had been planning to use.)

You can continue this down to much more tenuously bound systems. As I said, I hadn't thought about this until Eric Cornell talked about it, and he brought it up in the context of Cooper pairs in ultracold gases, which is in turn an analogy to the BCS theory of superconductivity. In this theory, electrons in a superconductor (or atoms in a gas of ultracold fermions) can "pair up" through weak interactions with other particles in the system, forming composite particles that are then treated as bosons. The superconductivity transition can be thought of (fairly loosely) as forming a BEC of these Cooper pairs (after Leon Cooper, the "C" in "BCS theory").

Cooper pairs in superconductors have binding energies in the milli-electron-volt range, so well below the level of room temperature thermal energy. This is why superconductivity is a low-temperature phenomenon-- you need to get the thermal energy down low enough that you can safely treat the weakly bound pairs as single particles, and not worry about them falling apart spontaneously. In ultracold atom systems, the binding energies are even lower, thus the need to be in ultracold systems. The same interactions could, in principle, pair up atoms at higher temperatures, but the pairs would get broken up as quickly as they formed, so a particle description just doesn't make any sense.

So, that's a longer than strictly necessary description of how and why we can get away with thinking of atoms and molecules as single particles, even though they're made up of smaller things. It all comes down to the energy available in the problem, and as long as you're dealing with low enough energy to keep your sample from breaking apart, it's okay to talk about even extremely complicated objects as if they were simple (albeit quantum) particles.

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(Astute observers might notice that there's one aspect of this I didn't talk about, namely why these composite particles have a de Broglie wavelength equal to what you would expect for a single particle of that mass, when they're composed of many much smaller particles whose de Broglie wavelengths would be many times longer-- a single atom in one of Arndt's big floppy molecules ought to have a wavelength around 400 times longer than the wavelength of the whole molecule, but the wavelength describing the interference pattern is the short molecular one, not the long atomic one.

(I didn't talk about this because I don't have a great answer. If you put a gun to my head an insisted that I make one up, I'd wave my hands and talk about Fourier series-- maybe when you add all those component wavelengths together in an incoherent way, you end up with something that looks like a shorter wavelength. But I haven't ever seen that bit explained, or thought about it all that much, so I don't know. This will likely bug me for a while, though, and if I come up with anything, I'll be sure to post about it.)

drorzel Tue, 10/15/2013 - 04:24

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So in response to your bracketed comment... I've admittedly never worked out the details of this, but I suspect is that you can just choose the center of mass as your degree of freedom just as you would in classical physics and that justifies treating a complicated atom as a point particle.

If you work in the Heisenberg representation, then instead of using X_i (i=1,...,N where N is the number of particles) as the operators that you evolve, you could use the center of mass X_CM and the relative positions X_12, X_23, etc as your degrees of freedom. Then since Heisenberg's equations are just the classical equations of motion, the Heisenberg equation for the center of mass operator should be the same as the classical equation of motion for the center of mass: namely, X_CM should act like a point particle, with a mass given by the total mass of the system, that only responds to the external potential. What gives me hope that there won't be issues about things not commuting is that the center of mass operators is just a linear combination of the original position operators and doesn't involve any momentum, but I've never worked through it so maybe you pick up hbar-suppressed correction terms somewhere.

Then if you go back to the Schrodinger picture, the wave function for the center of mass should act like a single quantum particle, with a mass given by the total mass of the system. Then the de Broglie wavelength for the center of mass wave function would obviously be given by the total mass of the object.

Then the idea would be that, so long as the energy of the whole system is dominated by the center of mass degree of freedom, then it is safe to treat the whole object as a single point particle.

I know it works out fine in the case of two particles, there's a problem about this in Griffifths (5.1) for the case of 2 particles.

@Andrew: I think you have to be careful about how you do that calculation. For the N-particle case you have 3N total degrees of freedom: three for the CM, three for angular orientation (assuming the molecule is not linear), and the remaining 3N-6 are vibrational modes. Since the angular orientation operators (like the others) are linear combinations of the individual particle position operators, that shouldn't be a problem (but if you screw it up, you could get angular momentum operators in there). The question is what to do with the zero point energy of those 3N-6 harmonic oscillators. I think that's a solvable problem involving a suitable definition of reference energy, but like you, I haven't actually done it. Note, however, that these modes do have a zero point energy, whereas the CM and orientation operators do not.

Just wanted to say I really liked this post. I just gave a guest lecture talking about energy scales for our physical chemistry lab class and I think I blew the students' minds by using K as a unit of energy. The exponent of k_B is pretty easy to remember because it's about equal to 1/N_A (Avogadro's number), which will get you to 10^-23. That's because k_B = R/N_a where R is the ideal gas constant. R is about 8 when the units are in J and N_A is about 6e23, which will give you about 1e-23. That's how I remember it, anyways. The number I personally find more useful is k_B = 0.7 cm-1/K, but that's because I did infrared spectroscopy for my PhD.

Chad,
About that wave business at the end of your post:you might start with plancks law that energy is proportional to frequency. The mathematical principle would be that the sum of two sine waves is equal to a product of sine waves with frequencies being the sum and difference of the frequencies of those two waves.

Perhaps your readers will find Walter Levins' Waves and Vibrations lectures a helpful refresher.
http://web.mit.edu/physics/people/faculty/lewin_walter.html

The relevant lecture would be #8
https://www.youtube.com/watch?v=_Fz0PSbew0g

Laser-Cooled Atoms: Strontium

drorzel — Mon, 26 Aug 2013 07:47:44 +0000

Laser-Cooled Atoms: Strontium

Element: Strontium (Sr)

Atomic Number: 38

Mass: Four stable isotopes, ranging from 84 to 88 amu

Laser cooling wavelength: Two different transitions are used in the laser cooling of strontium: a blue line at 461 nm that's an ordinary sort of transition, and an exceptionally narrow "intercombination" line at 689 nm.

Doppler cooling limit: 770 μK for the blue transition, below a microkelvin for the red. The Doppler limit for the red line turns out not to be all that relevant, as other factors significantly alter the cooling process.

Chemical classification: Alkaline earth, column II of the periodic table. Another greyish metal, but unlike the alkalis, it has not one but two electrons in its outermost shell. This is what leads to the "intercombination" line business above-- in two-electron atoms, the atomic states get sorted into two classes based on the relative spins of the two electrons, and transitions between states of different character are strongly suppressed. The red line used for cooling strontium is one such transition, which accounts for the ultra-low Doppler temperature.

Other properties of interest: Unlike most other laser-cooled species, strontium atoms have only a single ground state, which means that Sisyphus cooling doesn't work, and you're genuinely limited to the Doppler cooling limit. Which is why the red line is important-- a MOT on the blue line produces a cloud of atoms with a temperature around a millikelvin, which isn't that useful.

History: Laser cooling of strontium started surprisingly early (well, surprisingly to me, anyway), in 1990, in Japan. I'm not quite sure why they initially decided to pursue that in particular, unless they just happened to have a blue laser they were itching to put to use. It has since become moderately popular-- it's no rubidium, mind, but a surprisingly large number of groups are working with it-- in large part because of the ultra-low temperatures you can reach with the red line. The arxiv includes a very nice review from an Italian group in 2006.

Interest in strontium really took off in the later part of the 1990's, when Hidetoshi Katori's group in Japan came up with the "magic wavelength" idea (at least, I never heard of it before I visited their lab in 1998), which allows efficient loading into an optical trap by using a very particular wavelength that produces an identical light shift in both ground and excited states. This allows you to continue to laser-cool the atoms with the red line while loading them into the dipole trap. That, in turn, lets you create a sample that's tantalizingly close to BEC purely with laser cooling.

Of course, the word "tantalizingly" is doing a lot of work, there: the density and temeprature are almost what you'd want for BEC, but you can't quite get there by the normal methods. It turns out that the collisional properties of strontium give the abundant isotopes a very low "scattering length," which means it takes an exceptionally long time to re-thermalize, and mucks up the evaporative cooling process. Of course, physicists love a challenge, so two different groups nearly simultaneously found a way to Bose condense it anyway, using a rarer isotope with better collisional properties, and sympathetic cooling with a fermionic isotope, which was also cooled to a degenerate Fermi gas, and a mixture of Bose and Fermi gases, both in the quantum degenerate state was made arounf the same time. The idea of directly laser cooling the gas to BEC remained an intriguing possibility, though, and a group in Austria finally managed it earlier this year (the popular article at that link is the source of the middle image at the top of this post).

Random fun things: Strontium is the element responsible for both this "trading card" series of posts and the "cold atom tools" series that preceded it-- between the direct laser cooling to BEC paper back in January and the more recent absurdly precise atomic clock (and a quantum simulator in such a clock to boot), I've had a bunch of strontium-related papers open in tabs for possible ResearchBlogging write-ups. They didn't get written, though, because the amount of background required just seemed too daunting. With these series as reference, though, I'll got back to them and finally do the write-ups. When I have time.

Art: The cartoon version of strontium is a deranged Scotsman waving fireworks, and the Comic Book Periodic Table includes cover illustrations for both "Strontium Dog" and "Strontium Bitch." Thus satisfying both genders of canid. Or something. I don't know, comics are weird.

drorzel Mon, 08/26/2013 - 03:47

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Ahem.. Strontium (Sr)

Aaargh. Fixed now.

(You've stumbled across my high-tech method for formatting these: I cut-and-paste the previous post into the editor, then overwrite (most of) the text....)

Laser-Cooled Atoms: Sodium

drorzel — Mon, 19 Aug 2013 08:12:33 +0000

Laser-Cooled Atoms: Sodium

Element: Sodium (Na)

Atomic Number: 11

Mass: one stable isotope, 23 amu

Laser cooling wavelength: 589 nm

Doppler cooling limit: 240 μK

Chemical classification: Alkali metal, column I of the periodic table. Like the majority of elements, it's a greyish metal at room temperature. Like the other alkalis, it's highly reactive, and bursts into flame on contact with water. For this reason, all physicists working with sodium have True Lab Stories about accidentally blowing stuff up with it.

Other properties of interest: Scattering length of around 80 a₀; Feshbach resonance at around 900 G.

History: Most of the early laser-cooling experiments with neutral atoms (note: Dave Wineland did laser cooling of ions well before this, but that's a slightly different game) were done in sodium in the early-mid 1980's. This was largely technological, I think: at the time, the best tunable laser sources were dye lasers, and the rhodamine 6G laser dye allows reasonably reliable production of light at the sodium wavelength without being incredibly noxious (by the standards of laser dyes, at least). The first demonstrations of Zeeman slowing of a beam and sub-Doppler temperatures in optical molasses were made in sodium (and you can read the original papers via this Physics Focus article). Sodium was also the first cold atom magnetically trapped, and the atom used for the first MOT.

It was not, however, the first atom cooled to Bose-Einstein Condensation-- rubidium has that honor. It was close behind, though, with the Ketterle group successfully achieving a BEC of sodium a few months after Cornell and Wieman got BEC in rubidium (the NIST group, where I was working at the time, got BEC in sodium a couple of years later). Ketterle earned his share of the 2001 Nobel by racking up a whole bunch of "firsts" with the sodium BEC machine-- interference of two separated condensates, in-situ imaging of a condensate, demonstration of Feshbach resonances-- mostly because in the early days, they were able to make larger condensates than the Rb folks were, so certain kinds of measurements were much easier for them.

Sodium is considerably less popular these days, because while rhodamine 6G relatively well-behaved for a laser dye, it's still a gigantic pain in the ass to work with, and there are much more user-friendly solid-state laser sources-- diodes and Ti:Sapph lasers-- available now. (I'm not aware of anyone doing sodium cooling with doubled IR lasers, but I'd be a little surprised if nobody's tried it...) Other atoms also offer greater versatility, with multiple stable isotopes and more complicated level structures-- sodium's a pretty vanilla atom, other than the explode-in-water thing. But sodium's place in the history of physics is forever assured due to its central role in the development of laser cooling and BEC.

Random fun things: A long time ago, Bill Phillips was (mis)quoted by the New York Times as saying "Of course, there are no two-level atoms, and sodium is not one of them."

Art: The cartoon version of sodium is a chubby dude in a bathing suit. Most of the comic book treatments play off the explosiveness (greatly overstating the danger, by the way...).

drorzel Mon, 08/19/2013 - 04:12

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Know Your Laser-Cooled Atoms

drorzel — Mon, 19 Aug 2013 07:18:10 +0000

Know Your Laser-Cooled Atoms

At the tail end of the cold-atom toolbox series, I joked about doing a "trading card" version shortening the posts to a more web-friendly length. In idly thinking about this, though, it occurred to me that if one were going to have cold-atom trading cards, it might make more sense to have them for the atoms, rather than the techniques. And having just devoted many thousands of words to technique, I don't really feel like trying to cut those down more, but atoms...

The "featured image" up top is a slide from my laser cooling lectures for our first-year seminar class. Elements outlined in red have been laser cooled; the highlight colors within the boxes indicate different groups of atoms that are interesting for some common reason. I show this in class both to brag about the number of atomic species that the techniques I talk about can be applied to, and also to remind students of the vast swathes of the Periodic Table that are, as yet, unexplored in the ultracold regime.

I last gave this set of lectures in 2011, so the slide's a bit out of date-- in particular, dysprosium has not only been laser cooled, but Bose condensed since I last updated this. And even the out-of-date version has more atoms than I'd have the patience to write up individually. But we'll give this a go for a little while, at least, which should be enough to cover the really important atomic species from the history of laser cooling. Which ought to be enough to make a point of some sort.

I'm not going to do these all at once (though there will probably be a few in a row in the next couple of days, to get the ball rolling), but I hope they'll provide a source of quick-and-easy blog posts for the next little while that will hopefully be at least somewhat interesting to read.

drorzel Mon, 08/19/2013 - 03:18

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erbium has been condensed too, hasn't it? I wonder why radon hasn't. It's radioactive, but compared to say francium, it's practically stable.

Cold atom or laser cooled? If it's cold atom, please don't forget hydrogen...

-dan

Tools of the Cold-Atom Trade: Atom Detection and Imaging

drorzel — Fri, 16 Aug 2013 07:58:01 +0000

Tools of the Cold-Atom Trade: Atom Detection and Imaging

This is probably the last trip into the cold atom toolbox, unless I think of something else while I'm writing it. But don't make the mistake of assuming it's an afterthought-- far from it. In some ways, today's topic is the most important, because it covers the ways that we study the atoms once we have them trapped and cooled.

What do you mean? They're atoms, not Higgs bosons of something. You just... stick in a thermometer, or weigh them, or something... OK, actually, I have no idea. They're atoms, yes, but at ultra-low temperatures and in very small numbers. You can't bring them into physical contact with anything at cryogenic temperatures, let alone room temperature, without destroying the ultra-cold sample completely. And there are so few atoms-- several billion if you're dealing with a pretty healthy MOT down to a few thousand for a small BEC-- that it would take years of operation to accumulate enough to produce a lump measurable on even a highly sensitive laboratory scale.

But if you can't touch them, how do you study them? Well, the same way we study the properties of atoms in any other context: we bounce light off them. They still absorb and emit very specific frequencies of light, and we can use that fact to detect the presence of trapped atoms, measure their temperature, and even take pictures of their distribution. Essentially everything we know about ultra-cold atoms comes from looking at the light that they absorb and re-emit.

So, basically, you turn the MOT lasers on, and take pictures like in that famous picture? That's the simplest and earliest technique people used to study laser-cooled samples, yes. And, in fact, most of the early measurements were done using fluorescence in one way or another, generally just by measuring the total amount of light scattered from the atoms. The total fluorescence is, to a first approximation at least, proportional to the number of atoms in your sample.

Could you be a little more specific? Well, the first temperature measurements were done by a "release and recapture" method: they cooled atoms in optical molasses, measured the amount of light scattered from the could, then turned off the lasers for a short time. When the light was off, the atoms would drift away from the trap, and when they turned the lasers back on, they would get less total light, because they only recaptured some of the atoms. The number recaptured depends on the amount of time the lasers were off and the velocity of the atoms, so you can use that to measure the temperature.

That makes sense. So this is how you know the atoms are really cold? It's the first way people used to do the measurements. It has a bunch of problems, though, chiefly that you need to know the size of the laser beams very well, and have a sharp end to the trapping region. That's hard to do, so those measurements had a big uncertainty.

When the first sub-Doppler temperatures were measured, the NIST group didn't believe that they could possibly be getting atoms as cold as their initial results suggested, so they invented a bunch of other ways to measure the temperature. The best of these was the time-of-flight method, which became the new standard for a while.

How does that work? Well, you turn off the lasers that do the trapping and cooling, and turn on a single beam, positioned a bit below the trap. The released atoms will fall down through this beam, and when they do, they will absorb and re-emit light. If you measure the total amount of fluorescence from this laser as a function of time, you can use that to get the average speed of the atoms in the sample.

You can? Yep. See, the atoms in the trap are all moving in random directions, so some of them will be headed down, and some headed up. The ones headed down will get to the beam a little early, while the ones headed up with straggle in later. This gives you a fluorescence signal that has some "width" in time that's related to the spread in vertical velocities, which is the temperature.

You said it was the standard for a while, implying that it's not, now. Why is that? Well, the time-of-flight method is way better than release-and-recapture, but it still has problems. The time that you see depends a bit on the width of the beam, so you need to know the size and shape of the laser pretty well. The signal you get from any of these florescence based techniques also depends on the intensity of the laser, and any scattered light from elsewhere in the chamber-- so a little bit of flickering in the beam or a scratch on a window can throw things off. In the mid-90s, most diagnostics shifted to an imaging-based method instead, that involves taking pictures of the atoms.

So you take pictures of the light scattered by the cloud? Actually, the reverse-- you take pictures of a laser, and look at the light that's missing because the atoms absorbed it.

Excuse me? You look at light that isn't there? Right. The scheme looks like this:

Schematic showing the absorptive imaging method.

You take a single collimated beam of light at the frequency the atoms want to absorb, and shine it straight through the cloud of atoms onto a camera (with some lenses in there to do any magnification that you might want). The atoms will absorb light from the beam, and scatter it out randomly in other directions, so they cast a sort of "shadow" in the beam. The depth of the "shadow" depends on the total number of atoms along a line running through that part of the cloud, so you can get a density profile of the atom cloud. The data you collect look like this:

Sample images with and without atoms, and the subtracted image used to study BEC. From an old talk.

(which is also the "featured image" up above). You take two pictures: one image of the laser beam by itself, and one of the laser beam with the atoms present. Then you take a difference between those two images (subtracting pixel values in the software program of your choice), and that gives you an image of the density profile of the cloud of atoms.

Hey, that's pretty nice. Why didn't they do this from the beginning? Well, I suspect technology has a lot to do with that-- the method needs a decent CCD camera, which didn't start to get cheap until around the time I entered grad school. This method actually dates from pretty much my start at NIST, actually- the optical control of collisions paper that was my first article in grad school used to get cited a bunch for explaining this method; I'm not sure we were the first to do it, but we were one of the first in print.

So, these pictures are useful, then? Oh, absolutely. There's a ton of information in these-- you get the complete density profile, so you can extract an accurate measurement of the size of the cloud, and thus the peak density in absolute terms. You can measure the temperature by taking several of these images at different times after turning off the trap lasers, and watching the cloud expand-- the change in shape tells you the average velocity. You can even detect some cool effects by the way they change the density profile.

Such as what? Well, Bose-Einstein condensation. The famous three-peak image that headed the evaporative cooling post shows the first detection of BEC, which was detected by the density profile. Here, I'll put it in again:

The signature image of a cloud of rubidium atoms crossing the BEC transition, from the Nobel Prize site.

This is a set of three density profiles turned into three-dimensional pictures for gosh-wow value. The picture on the left shows a cloud at a temperature above the BEC transition, and is basically a smooth-ish lump of atoms in a mostly spherical cloud. The middle picture, though, has a big blue-white spike sticking up in the center-- that's the BEC. The condensate is at a much, much lower temperature (in terms of the thermal velocity of its atoms) than the original cloud, and shows up as a very dense lump in the center. It's also lopsided, because the TOP trap they used is not spherically symmetric, and the shape of the BEC spike corresponds nicely to the shape of their trap, as it should.

And the picture on the right? That's a cloud well below the transition temperature. Where the middle picture, just barely below the transition, has a two-part profile-- the smooth thermal cloud and the sharp BEC spike-- the third picture is pretty much just BEC. Showing that you can make nearly pure condensates by evaporative cooling in the magnetic trap.

Very nice. One question, though: Why did they color empty space red, and the condensate blue-white? I have no idea. They're about the only people ever to use that color map. Everybody else uses blue/black for empty space, and orange-yellow for the condensate.

And this is the standard technique for measuring BEC? It gets the basic idea, yes. There are some refinements to it-- the absorption technique is destructive, in that the condensate atoms have to absorb light to be detected, and when they do, they get a momentum kick that blasts the condensate apart. So if you want to measure time--dependent behavior this way, you need to piece it together from lots of individual images of different condensates.

You can improve on this somewhat with a couple of other techniques that basically just reduce or eliminate the photon scattering by the BEC-- there's a "phase contract" technique, for example, that relies on using off-resonant light (so the condensate atoms don't absorb) and treating the condensate like a medium with some index of refraction that phase-shifts the light passing through it. With a bit of clever optical design, you can turn that into a "non-destructive" image of the condensate, which the Ketterle group pioneered and used to do the first in-situ studies of condensates in traps.

The basic idea of all of this is the same, though: you shine a laser through the condensate onto a camera, and use its effect on the light to take a picture of the density profile of the cloud.

And this is the only tool you have for measuring things? Pretty much. But it's a very powerful tool-- most of the things you'd like to see cause changes in the density profile. This slightly outdated image collection from MIT for example, has some nice pictures of vortices, where the rotational motion of a condensate flowing in a trap show up as "holes" in the density distribution. You can also turn position measurements into momentum mesaurements by giving the cloud a really long time to expand-- at that point, the position of the atoms is really a measurement of their initial momentum, which determines what direction they move and how quickly.

The imaging technique can also be state selective, because different atomic states will absorb slightly different frequencies. So you can get pictures that show each of two different states separately, or that tag the state in some way. That's essential if you want to do quantum computing sorts of experiments.

There are still experiments using fluorescence imaging, too-- most of the direct-imaging studies of atoms in optical lattices use fluorescence to detect the individual atoms. And if all you care about is a single number, fluorescence detection is much simpler and faster, so atomic clocks tend to use that.

But it's all light scattering, all the time? For certain types of experiments, there are other kinds of detection that work-- some kinds of collisions produce charged particles, for example, and those can be detected with high efficiency. The metastable atoms I studied in grad school have enough energy to knock electrons loose from a surface, so we used to detect them by dropping them on a micro-channel plate. But those are really special cases. The vast majority of what we know about the physics of cold atoms comes from shining light on them and looking at either what comes out, or what doesn't come out.

But then, this isn't too surprising, as the vast majority of everything that we know about atoms comes from bouncing light off them. Cold-atom physics just has a couple of specialized methods for doing this, that happen to work well because the atoms really aren't moving very much at all.

So, that's it for this series, then? Pretty much, I think. There are some other tricks that turn up occasionally in the field, but I think we've covered all of the really general stuff that's shared by nearly all cold-atom experiments. I hope this will end up being a useful resource-- if nothing else, it gives me a set of links that I can paste into future posts when some core technique is important but I don't want to take time to explain it.

You should also do a trading-card version, dude. Some of these are pretty long. Yeah, well, I like to talk. But we'll see about doing a quick-reference variant. In my copious free time.

But for now, that's it. I hope this has been helpful and/or interesting.

drorzel Fri, 08/16/2013 - 03:58

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Thanks for doing this series, it's been really interesting to follow along. Keep up the blogging, you explain this stuff really well.

This series has been good, yes. I didn't know about the density profile imaging method -- is there a simple term for that method?

Tools of the Cold-Atom Trade: Evaporative Cooling

drorzel — Thu, 15 Aug 2013 07:33:53 +0000

Tools of the Cold-Atom Trade: Evaporative Cooling

In our last installment of the cold-atom toolbox series, we talked about why you need magnetic traps to get to really ultra-cold samples-- because the light scattering involved in laser cooling limits you to a temperature that's too high for making Bose-Einstein condensation (BEC). This time out, we'll talk about how you actually get to those ultra-cold temperatures.

What do you mean? I assumed it was just part of the trapping process? No, because the forces involved in magnetic trapping are like those involved in optical dipole traps. In physics jargon, they're "conservative" forces, which can't produce cooling-- a sample of atoms in the trap will just move back and forth with constant total energy. To get cooling, you need a dissipative force, like the absorption and emission of photons in laser cooling.

But I thought you said you couldn't use photon scattering to get to BEC? Right, so you need to find another way to introduce dissipation into the system. Without using laser light to do it, because of the heating induced by photon scattering.

In the end, it turns out that there's really only one thing you can do: you can throw atoms out of the trap.

Yeah, but how does that help you? Just removing atoms at random doesn't help, but if you can selectively remove the fast-moving atoms, you can cool your sample.

Wait, fast-moving atoms? I thought these were all cold atoms? Well, fast is a relative term. The important thing here is that, as we discussed a while back regarding that "negative temperature" paper the temperature is a property of a distribution of atoms. The temeprature is simply related to the average kinetic energy of the sample, but the atoms don't all have the average energy-- instead, they're distributed over a range of energies about that average.

This means that no matter how cold the temperature of the sample is, there will always be some atoms with energies above the average energy. And if you can selectively remove those atoms, they take away a greater-than average amount of energy from the sample as a whole, meaning that the average energy of the remaining atoms is necessarily lower.

Yeah, but how is this possible? Isn't removing the fast-moving atoms a Maxwell's Demon sort of problem? I thought that was impossible. It's not impossible to set up a Maxwell Demon, just highly improbable. There's nothing in principle wrong with the idea-- what's impossible to do with a demon is to reduce the entropy of a gas without producing a corresponding increase in the entropy of the rest of the universe. If you work it all out, it turns out that the action of the "demon" will necessarily produce an increase in entropy that matches or exceeds the decrease in entropy of sorting the atoms by speed, so everything is okay.

But that's unnecessarily complicated-- it turns out that you don't need quasi-omniscient anthropomorphic personifications to make this work, just a clever use of your magnetic trap. Specifically, the fact that your trapped atoms are in one particular internal state, and there are other states out there that are not trapped.

How does that help? Well, the cartoon version looks like this:

Cartoon version of evaporative cooling in a magnetic trap.

The blue and green lines represent the internal energy of an atom in the trapped and untrapped states, respectively. Initially, all the atoms are in the trapped state, which has a shape resembling a sort of bowl (in reality, it's usually a parabola, but I drew this quickly and didn't make the shape all that accurate). The atoms in the sample move around in this bowl, basically "sloshing" back and forth, turning around when their total energy matches the internal energy (because once all the energy available to the atom has gone into internal energy, it has to have zero kinetic energy-- that is, come to a stop for an instant).

The key realization is that the "hot" atoms (red circles) reach their turning points farther out from the center of the trap than the "cold" atoms (blue circles). Which means if you want to selectively remove "hot" atoms, you just need to remove those atoms that reach the outer edge of the trap.

Yeah, but how do you do that? That's where the untrapped states come in. If you do something to flip the atom from the trapped state to the untrapped state, it will feel a force pushing it away from the center-- the internal energy looks like the green curve, rather than the blue, and it can reduce that energy by moving away. And you can selectively change the state by using radio-frequency light.

I thought you said you weren't allowed to have any light? I said you couldn't have laser light. The RF photons used for evaporation are so low-energy that they don't change the momentum of the atoms significantly. And anyway, the only atoms interacting with them get removed from the trap.

But how do you select the "hot" atoms to remove? By the frequency of the light. See, to drive an atom from one state to the other, you need a frequency that matches the energy difference between the two states. That difference depends on the magnetic field, which depends on the position. Out near the edge of the trap, the energy difference is big, so you need a high frequency to flip the state, but closer to the center the energy difference is small, and the frequency is lower. You can basically dial in the position at which you remove atoms, and thus the energy of the atoms being removed, by choosing the frequency of RF that you apply.

That sounds... almost too good to be true. It's a little trickier than that description makes it sound, but it works very well. People in the field refer to it as an "RF knife," as if you're shaving away the atoms at the outer edge of the cloud. And if you use a TOP trap, you get an extra bonus bit of evaporation from the zero-field point, which orbits the center of the trap in a circle of some radius. Atoms crossing that "circle of death" can flip their state to the untrapped state as well, and again, this selectively removes atoms in the outer part of the trap, taking away the hot atoms.

But once you've removed the hot atoms, aren't you done cooling? I mean, they're gone, so what do you do next? Well, there are a couple of things that happen at that point. One is that the atoms collide with each other, and "re-thermalize." The total energy of the sample decreases because you've taken the hot atoms out, leaving a sort of truncated thermal distribution. collisions between atoms will redistribute this energy a little bit-- sometimes when two low-energy atoms collide, one will end up with higher energy, while the other moves to lower energy-- and pretty soon, you have a thermal distribution matching Maxwell-Boltzmann distribution again.

Then you can remove the highest-energy atoms from that, by reducing the frequency of the RF knife a little bit. That moves the point where you're taking atoms out in, and lowers the energy of the atoms you're removing. But they're still the hottest atoms in the trap, so the temperature decreases. And you re-thermalize again, and move the frequency again, and so on.

That's pretty slick. Yeah, it is. It's trickier than that description sounds, of course-- the thermalization depends on the collisional properties of the atoms, and there are both "good" collisions that redistribute energy and "bad" collisions that randomly remove atoms from the trap, so you have to make sure there are more good collisions than bad. But in the end, this process gets you lower temperature. And, incidentally, an increase in density, which you also need for BEC. So it's a great method all the way around.

Wait, how does it increase the density? The colder atoms left behind take up less room in the trap, because they have their turning points closer to the center. Meaning they're packed into a smaller volume, and thus have a higher density.

This still sounds too good to be true. Are you sure this is legal? It absolutely works, I swear to you. This is the means by which dozens of groups all over the world produce BEC, probably hundreds or thousands of times in a typical day.

But you don't need exotic physics experiments to prove that this process is physically allowed. Just go get a cup of coffee or tea, and don't drink it.

Don't drink it? Right. If you don't drink it, but just let it sit there, some time later, you'll come back to cold coffee or tea. This happens in part because of a process very similar to what cold-atom physicists do to make BEC: the "hottest" molecules in the hot coffee evaporate away as steam, and the molecules left behind have lower energy, and thus a colder temperature. That gives the process its name, "evaporative cooling."

But, but... Entropy? To be honest, I've never thought about the thermodynamics of this in all that much detail; since it undeniably works to make BEC, I feel safe in assuming that the entropy of the universe has increased as a result of this process, even as the condensate itself forms a low-entropy state. The decrease in the entropy of the atoms that go into the condensate is matched by an increase in the much greater number of atoms that left the trap, plus the RF photons and whatever else.

OK, I guess. But that brings up another point: doesn't this involve throwing a whole bunch of atoms away? Absolutely. The initial MOT that people load into a magnetic trap for evaporative cooling will usually have something like a billion or ten billion atoms. A million-atom BEC is a pretty healthy size, so you're throwing away around 99.9% of the atoms you start with in order to get the final BEC.

But that's the price you have to pay to get to those temperatures. And a million atoms is still plenty to work with to study the properties of BEC and the other cool quantum effects that it lets you explore.

I guess so. But, hey, you also alluded to making BEC in optical traps. How does that work? The basic principle is the same-- they do evaporative cooling. They generally don't use RF evaporation, though, because the size of the traps and the energy level shifts are different. Instead, they just provide a way for the trapped atoms to "leak" out of the trap, provided they have high enough energy. Then they can reduce the laser intensity, lowering the energy limit, evaporating hot atoms just like in a magnetic trap.

Optical traps tend to be smaller, so the collision rate is higher, and when you work it all out, the evaporation process proceeds faster, but the idea of the process is essentially the same: throw out hot atoms, keep cold ones.

If you want to play around with it, they have a cool little game at the Physics 2000 project at the University of Colorado. It requires Java, though, which might almost be more hassle than it's worth for the fun of evaporatively cooling simulated atoms.

So, how do you know when you've made a BEC? Do you stick in a thermometer, or something? No, you just take a picture of the atoms. These then get turned into three-dimensional plots of the density profile, like the famous shot that Cornell and Wieman used to announce they had gotten BEC, which is the "featured image" at the top of the post. The making and interpretation of those images is a critical part of cold-atom physics, but we'll save that for another post. Any other questions before then?

Just one: Can I drink this coffee now, before it evaporates away to BEC? Sure, go right ahead.

drorzel Thu, 08/15/2013 - 03:33

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Tools of the Cold-Atom Trade: Magnetic Traps

drorzel — Wed, 14 Aug 2013 07:57:19 +0000

Tools of the Cold-Atom Trade: Magnetic Traps

We're getting toward the end of the cold-atom technologies in my original list, but that doesn't mean we're scraping the bottom of the barrel. On the contrary, the remaining tools are among the most important for producing and studying truly ultra-cold atoms.

Wait, isn't what we've been talking about cold enough? There is, as always, more art than science in the naming of categories of things. "Cold" and "ultra-cold" get thrown around a lot in this business, and the dividing line isn't quite clear. Very roughly speaking, most people these days seem to use "cold" for the microkelving scale temperatures you can get with magneto-optical traps and optical molasses, but reserve "ultra-cold" for the sorts of temperatures you find in Bose-Einstein Condensates.

And those are lower than a millionth of a degree above absolute zero? Yeah. BEC itself, at least in dilute atomic vapor systems, gets into the regime where it doesn't quite make sense to talk about temperature-- you're not going to get any closer to absolute zero than that, so what "temperature" you assign to it is just a matter of how patient you're willing to be when expanding your trap to lower the energy of the lowest state. But the transition temperature where BEC occurs is well below a microkelvin-- the exact number depends on the density of atoms in the trap, but it's generally in the nanokelvin kind of range.

An you can do this all with lasers? Yes and no. You can make BEC by all-optical methods-- collecting atoms in a MOT, cooling them with molasses, and loading them into a dipole trap for the final cooling. That can work very well, and is the fastest current path to BEC. But it wasn't the first technique used-- in fact, the first BEC experiments dispensed with lasers altogether for the final steps.

Why is that? I thought laser cooling was the key? Laser cooling is the key technology for enabling the production of BEC, but except in certain very unusual cases, laser cooling alone can't get you to BEC. The problem is that laser cooling works by scattering photons, and transfers momentum to atoms in (very roughly speaking) multiples of the momentum of a single photon. This means it's extremely difficult to get to temperatures lower than the "recoil temperature" corresponding to a sample where all the atoms have, on average, the momentum of a single photon of light at the cooling frequency. That can be very cold-- hundreds of nanokelvin for rubidium-- but it's still too high to reach BEC at the densities you can get in a MOT. Those densities are also limited, because when you start to pack lots of atoms in a confined space, when one atom emits a photon, it can be re-absorbed by another atom in the sample before it leaves. That tends to screw up the cooling a tiny bit, and also creates a kind of outward force pushing the atoms apart, getting a lower density.

To reach BEC, you need a different means of cooling and trapping atoms, one that doesn't involve the atms absorbing and emitting photons.

And going by the post title, I expect this will involve magnets in some way? Right. Historically, the first BEC's were produced in magnetic traps, with no lasers at all. The essential physics here is something we've mentioned a few times already in this series, the Zeeman effect. When you apply a magnetic field to the atoms, it shifts the energy of the electrons in the atom around.

Now, in both of the previous mentions of this, we've talked about the Zeeman effect changing the frequency of light that atoms want to absorb. But if you're not concerned about light, and have an atom with more than one sublevel in the ground state, you can use this to push atoms around with magnetic fields. The energies of those ground-state sublevels will shift as you apply a magnetic field.

So it's like the light shift making a dipole trap? Similar. The light shift involves an oscillating field (it's also sometimes called the "AC Stark effect," because the shift of energy levels due to an electric field was discovered by Johannes Stark (who later became a creepy Nazi, but that's a different subject)). The Zeeman shift involves constant magnetic fields, and only affects states with non-zero angular momentum. If you've got an atom with more than one sublevel in the ground state, though-- and nearly all of the atoms people laser cool have this property-- you'll have some sublevels that shift up in energy as you increase the magnetic field, and others that shift down in energy.

So, like with the light shift, you just create a region of space with a big magnetic field in the center, and the atoms get trapped there? It would be nice if you could do that, but in fact, you can't create a stable maximum of magnetic field in empty space. If you could, then you could create a region where the atoms whose energy decreases with magnetic field get stuck, and that would be nice. But that would violate a bunch of laws of physics.

Instead, you do the opposite-- it is possible to create a local minimum in the field in empty space, as you do in making a MOT, where the field is zero in the center and increases as you go out. This turns out to be really easy, just requiring two coils with currents in opposite directions (the "anti-Helmholtz configuration" in AMO jargon). If you make the field really big, that lets you trap the atoms whose energy increases as the field goes up-- their energy is lowest at the center of the trap, so they feel a force pushing them into that region.

And this lets you trap atoms without lasers, so you can use it to make BEC? Cool. Sadly, it's not quite that simple. Because you still have those other states running around, the ones whose energy goes down as you go to higher fields. If the atoms move into those states, then they can lower their energy by moving out of the center, and you're no longer trapping them.

So, how do you keep the atoms from flipping states? Well, for the most part, that happens automatically-- the property that determines whether a given atom increases or decreases energy with magnetic field is the angular momentum, and angular momentum is conserved. The analogy most people use, because it lets us play with cool toys, is the Levitron levitating magnet. You can set up a field just like that in a magnetic trap that would hold a permanent magnet off the ground, provided the magnet is in a particular orientation-- a ring of permanent magnets all with their north poles inward will do it. If you just put a magnet there and let it go, though, it will just flip over, at which point it's attracted to the ring, and falls. If you put that magnet inside a spinning top, though, the angular momentum of the top prevents it from flipping over, and you can levitate the magnet in space. Which makes a great party trick or lecture demo.

Atoms in a magnetic trap are the same way. They can't easily flip their states because of angular momentum conservation, so once you get them in the "low-field seeking" state that increases energy as the field goes up, they tend to stay there. Magnetic trapping works nicely, and was in fact demonsttrated in the 80's.

So you brought up a problem that isn't actually a problem? It's not a problem, unless you're trying to make BEC. See, the trapping state is defined by ts angular momentum, which is measured relative to some axis. That axis is defined by the magnetic field, so as long as there's an applied field, the atoms are in a well-defined state, and can't easily change it.

Right in the center of the trap, though, the field is zero. And when the field is zero, there's nothing to define the angular momentum relative to, which means an atom in the zero-field region can flip from one state to another (this is called a "Majorana transition," presumably relating to Italian physicist and international man of mystery Ettore Majorana). Which puts a big "leak" in the center of the trap. That's not a big deal if you're working with fairly hot atoms, which don't spend much time in the center, but when you try to make BEC, you want to create high density by packing all the atoms into a really small region, which unfortunately sits right on top of the "leak." At which point everything falls apart.

So you need some other clever trick to plug the "leak." Exactly. The first experiment to make BEC in rubidium, by Eric Cornell and Carl Wieman in Colorado (shown in the "featured image" up top), used a "Time Orbiting Potential" or TOP trap, which fixed the problem by adding an extra field that changed in time. You can't just add a constant field, because all that does is move the position of the zero around, but if you change the field quickly enough, the atoms can't follow it, and what they see is a sort of average field. The TOP trap used an audio-frequency field-- we used one for the squeezed state experiments I did at Yale, and the characteristic high-pitched whine of the TOP coils is one of my strongest memories of that lab-- that pushed the zero point out of the center and spun it in a circle. The central region then looked like a rounded bowl sort of potential, with a non-zero field at the center.

Another approach, used by Wolfgang Ketterle's group for the second BEC experiment, with sodium, is just to keep the atoms from being at the zero point by physically pushing them away. Ketterle used an "optical plug," a laser focused down to the central point of the trap, with its frequency tuned to push atoms away from the light. That created a sort of donut-shaped trap, partly due to the Zeeman shift and partly due to the light shift, that plugged the leak in the center of the trap.

That sounds really tricky. It was fairly difficult, I think, and never really became all that popular, though some groups still use it.

Can't you just make a different sort of trap that doesn't involve a zero in the middle? You can. but it requires a more complicated system of coils. There are several different approaches to this that have been used over the years-- a Ioffe-Pritchard trap, a "baseball" trap (because the coils to make it follow a pattern like the seams on a baseball), etc. All of them have the same general result, though: a magnetic field that is small but not zero in the center, and increases as you move out. There are pros and cons to all the methods, but they all work more or less the same way.

And all of these let you get to BEC? Yep.

How? The process is called "evaporative cooling," and is really the simplest sort of cooling scheme you can imagine. It's a little complicated to explain, though, and this is already almost 1900 words.

So, even though it wasn't on your original list, you're going to split it off into a new post. Yeah. Sorry about that.

drorzel Wed, 08/14/2013 - 03:57

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I'm really enjoying this series, even though much more than I'd like is going over my head. I'm doing my best though - it's my deficiency, not yours. I expect if I read them over a few times each, I'd get more of it.

I did want to say, however, that I love the little bits of humorous phrasing that you occasionally drop in. Little titbits like "Italian physicist and international man of mystery Ettore Majorana" make me chuckle and offset my self-disgust at not picking up these ideas more quickly, despite your excellent and engaging explanations.

Evaporative cooling? Ooh! Can I supply a "question" for your Q&A format?

"Wait, that sounds a lot like Maxwell's demon. Chad! In this lab we obey the laws of thermodynamics!"

Use or not, as you wish (though please do address the thermodynamic issue).

Tools of the Cold-Atom Trade: Magneto-Optical Traps

drorzel — Tue, 13 Aug 2013 08:04:41 +0000

Tools of the Cold-Atom Trade: Magneto-Optical Traps

Today's dip into the cold-atom toolbox is to explain the real workhorse of cold-atom physics, the magneto-optical trap. This is the technology that really makes laser cooling useful, by letting you collect massive numbers of atoms at very low temperatures and moderate density.

Wait a minute, I thought we already had that, with optical molasses? Doesn't that make atoms really cold and stick them in space? Molasses does half the job, making the atoms really cold, but it doesn't actually confine them. The photon scattering that gives you the cooling force and Doppler cooling limit produces a "random walk" kind of motion on the part of the atoms. When the atoms absorb a photon, they tend to slow their motion in the direction the laser came from, but when they re-emit that photon in a random direction, they get a "kick" in the opposite direction from the departing photon. That means they bumble around constantly changing the direction of their motion, like a drunk frat boy wandering around a crowded party.

That's an analogy that goes over well in class, I'll bet. Most of the time when I talk about this stuff, it's to first-year physics majors, so there's less underage drinking than you might think.

Anyway, while the molasses force creates a region that's sort of "sticky," it doesn't actually prevent atoms from leaving. Any atom that makes it to the edge of the laser beams is free-- with no more light, there's no more force, and it just floats away. in whatever random direction it was headed when it hit the edge.

Now, the molasses beams can be pretty large, so you can get a decent number of atoms-- several million, say-- but that's not actually that many in the grand scheme of things. If you want to get really large numbers of atoms-- billions, say-- you need to do something to keep the atoms from wandering away. You need a force that depends on the position of the atoms, acting to push them back toward some central region.

And you do that with magnets? How the hell does that work? Well, as the name suggests, you do it not just with magnets, but with light, as well. It's a magneto-optical trap, and the optics are key.

The idea is basically a combination of an optical molasses with a weak magnetic field that varies in position. That lets you exploit the internal states of atoms, and the rules for interacting with polarized light that we talked about in the Sisyphus cooling post to create a new force that confines the atoms.

That sounds kind of complicated. Yes and no. It brings a bunch of stuff together, but the end result is a surprisingly simple and robust tool. The simplest version looks like this, schematically:

Schematic of a one-dimensional magneto-optical trap.

Oooh! Pretty colors! Yeah, well, they all mean something.

This is a cartoon representation of the energy states involved in making a MOT, at least in one dimension. You start with the simplest sort of multi-state atom, that has only one ground state level (the dark horizontal line at the bottom), but three excited-state sublevels (the red, green, and blue lines up top). In the absence of a magnetic field, these three levels have exactly the same energy, but if you apply a field, they shift around, one going up, one going down, and one staying put.

Which of the three goes up and which goes down, though, depends on the direction of the field. So, if you take a magnetic field that's zero at some point in space and increases linearly to either side, you get a picture like the cartoon above: on the left, the atom is in a magnetic field that shifts the red state down and the blue state up. In the center, the field is zero and there's no shift, so all the levels have the same energy. On the right, the atom is in a magnetic field that shifts the red state up and the blue state down.

Where does this shift come from? We've mentioned it before, when we talked about the slowing of beams-- it's the Zeeman Effect, pronounced "ZAY-mon," because he was Dutch.

Fun trivia: when I was an undergrad learning about this stuff, there were two names for this rattling around: a lot of people called it a "Magneto-Optical Trap" or "MOT," but some, principally the Wieman group at Colorado, called it a "Zeeman Optical Trap" or "ZOT." I liked the sound of that better, so my undergrad thesis uses "ZOT," but in grad school I joined a group that used "MOT" and got some gentle mockery about that. "MOT" eventually won out overall, another sad example of physicists choosing the more boring of two possible names.

You guys really need to hire some English majors to help with your branding. Whatever.

So, these energy levels, they go up and down, but how does that help? The key trick is, remember, the polarization of the lasers you send in determines which state you can go to. Now, in this system there's only one ground state so optical pumping isn't an issue, but if you shine in a laser of, let's say, left-hand circular polarization, that will excite the atoms only to the blue excited state, while right-hand circular polarization will excite only to the red excited state.

This gives you a way to add a spatial component to your optical forces. You detune your lasers to an frequency below the natural frequency that the atoms want to absorb, as if they were going to a lower energy state indicated by the dotted line. Most of the time, there's no state there so atoms won't absorb it, but on either side of the center, there's a point where the state that shifts down crosses that line. At that point, an atom that's standing still will happily absorb photons from a laser of the appropriate polarization.

So you choose the polarization of the lasers in the molasses to match the level that's shifting down? Exactly. The big red arrow represents a right-hand circular laser coming in from the left, which will get absorbed by even an atom at rest when it reaches the vertical red arrow. When it absorbs the light, it feels a force to the right, back toward the center of the trap.

On the other side of the trap, on the other hand, you have a big blue arrow representing a left-hand circular laser coming in from the right, which excites atoms to the blue state at the position of the vertical blue arrow. That also produces a force back toward the center. So, atoms on either side get pushed into the center of the trap, and kept there when they try to leave.

And do you still get the optical molasses effect? Absolutely. The Doppler shift of the atoms changes the position where they feel the MOT force slightly, but you still get a molasses-type force when atoms move in either direction, cooling them. In practice, the Sisyphus cooling isn't as effective inside the MOT-- the magnetic field changes things a bit, and the laser detuning for minimum temperature is different than the laser detuning for most effective MOT operation-- but you get a large number of very cold atoms that are stuck in a small region of space.

So this is why people were shining lasers with opposite polarizations on their atoms and accidentally doing Sisyphus cooling? Part of the reason, yes. It was a very happy accident, brought about by a clever trick for exploiting the magnetic sublevels to do trapping.

So the magnetic fields trap the atoms in a particular place? No, the magnetic fields are much too weak for that-- you can trap cold atoms with magnetic fields alone, but that requires larger fields than a MOT. The magnetic field of the MOT just serves to define a region of space where the trap will be located, while the actual confining force comes from the absorption of laser photons.

A fantastic demonstration of this is this famous photo:

Kris Helmerson of NIST looking into the vacuum chamber at a sodium MOT.

That's Kris Helmerson, one of the staff members in the laser cooling group at NIST when I was there (he's now a professor in Australia) looking into the vacuum system at a sodium MOT. The bright orange dot right in the center is a MOT containing several billion atoms, which are visible because they're constantly absorbing and re-emitting photons from the lasers that provide the confining force.

How big are these traps? In principle, there's no real limit, provided you can make a big enough magnetic field and large enough laser beams. In practice, the clouds of trapped atoms tend to be something on the short side of a millimeter across.

So, you've got a billion atoms in a cubic millimeter? Isn't that awfully dense? Hardly. The density of a pretty good MOT might be on the order of 10¹² atoms per cubic centimeter, which sounds like a lot, but is around a billion times less dense than air. It's a really diffuse vapor, which is why all these experiments have to be done in ultra-high vacuum chambers.

That is, however, an exceptionally pure sample of atoms-- you can pick the specific isotope of whatever element you want to trap-- at extremely low temperatures, so it's a fantastic resource for atomic physics. The MOT was invented in 1986-ish, but by the mid-1990's had become absolutely essential for atomic physics-- you can use it as a source of atoms for high-resolution laser spectroscopy, ultra-precise atomic clocks, and all sorts of cool quantum stuff that uses the slow velocity of the atoms to explore new regimes.

And once you've got all these atoms, you just fiddle with the lasers and magnets to make a Bose -Einstein Condenstate, right? For extremely difficult values of "fiddle," I suppose. It's actually much more complicated than that, though-- the density you need for BEC is much higher than you can get in a MOT, and the temperature much lower, by orders of magnitude. There was a lot of really clever additional work involved in getting to BEC. A MOT is just the starting point.

And I bet this additional work involved some new technology that you'll describe in a future post... I guess I am a little predictable with this...

drorzel Tue, 08/13/2013 - 04:04

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pronounced “ZAY-mon,”

I'm not Dutch, but my modest knowledge of IPA certainly doesn't match that pronunciation.

Perhaps I need to learn to speak (American) English better.

@Sili: As you are probably aware, there were some vowel shifts in English which did not happen in any other Indo-European language. "ZAY-mon", as pronounced by native English speakers, is a reasonable approximation to the correct pronunciation of Zeeman. But only a native English speaker would indicate the pronunciation in that way.

The differences in pronouncing English and other European languages has occasional amusing results in US place names. Several US cities and towns are named after places in Europe, but by people who only saw those names in writing, not heard them pronounced. Thus, for example, Versailles, Indiana (stress the first syllable and pronounce the second like the English word "sails", whereas the French place it's named for has the stress on the second syllable, which sounds like the English word "sigh").

Tools of the Cold-Atom Trade: Optical Pumping and Sisyphus Cooling

drorzel — Thu, 08 Aug 2013 09:47:38 +0000

Tools of the Cold-Atom Trade: Optical Pumping and Sisyphus Cooling

This topic is an addition to the original list in the introductory post for the series, because I had thought I could deal with it in one of the other entries. Really, though, it deserves its own installment because of its important role in the history of laser cooling. Laser cooling would not be as important as it is now were it not for the fact that cooling below the "Doppler limit" in optical molasses is not only possible, but easy to arrange. That's thanks to the "Sisyphus cooling" mechanism, the explanation of which was the main reason Claude Cohen-Tannoudji got his share of the 1997 Nobel Prize in Physics.

So, you're finally going to explain those colder-than expected temperatures? Yep.

Took you long enough. Well, it's a complicated subject. It requires four pieces to work, three of which we've talked about at least briefly: one is that when you put multiple lasers together to make optical molasses, you can get patterns in the intensity and polarization of light, that are useful for making optical lattices, thanks to the second piece, the light shift changing the energy levels of the atoms. The third piece, mentioned briefly at the end of the lattice post, is that the atoms in question have multiple sub-levels, which can experience different light shifts.

The final bit is a phenomenon called "optical pumping."

Does this involve moving atoms through light pipes? No, "light pipes" are a completely different thing. Optical pumping is a way of moving a population of atoms between their internal states. By using the right kind of light, you can arrange to put nearly all of the atoms in a sample into a particular internal level of your choice.

The key to this is that light carries angular momentum that depends on its polarization. If the light has right-hand circular polarization, an atom absorbing the light not only acquires the energy of the photon, moving one electron to a higher energy state, it also increases the angular momentum of that electron by one unit. If the light has left-hand circular polarization, the angular momentum of the electron decreases by one unit. This moves an electron from one of the ground-state sublevels to a different sublevel in the excited state.

So you optically pump atoms into higher angular momentum excited states. But they don't stay in the excited state, so how does that help anything? They don't stay in the excited state, true, but when they drop back down to the ground state, they can only change their angular momentum by at most one unit-- they can go down one, up one, or stay the same.

This fact lets you move electrons into the maximum angular momentum state very quickly, through the absorption and emission of several photons. That's the "pumping" of optical pumping-- you use light to move all the atoms into one of the extreme states.

I don't follow. If the decay is random, how can you pump atoms in a particular direction? It helps to look at a cartoon of a simple example system. The simplest atom with multiple sublevels has two ground-state levels, and four in the excited state (these are labeled with half-integer values, for reasons that don't matter for our purposes):

Cartoon of optical pumping. Right-hand circular polarized light drives atoms into higher angular momentum states.

If you start with an atom in the negative angular momentum state and shine in right-hand circular light, you get the situation on the left: the atom absorbs a photon, and moves up in angular momentum as it goes to the excited state. From there, it can decay back to where it started (decreasing by one unit) or to the other of the two ground-state levels (dropping straight down, with no change of angular momentum). There's no higher-angular-momentum state for it to decay to, so it can't increase its angular momentum during the decay. If it goes back to where it started, it repeats the process, getting excited back up to the higher angular momentum state again.

If it decays to the other ground-state level, though, it's stuck. It can absorb a photon and go to the higher angular momentum excited level, but from there it can only go back to one ground-state sublevel. There's no state for it to decay to without decreasing its angular momentum.

This means that an atom starting in the negative-angular-momentum sublevel of the ground state will inevitably end up in the positive-angular-momentum sublevel when exposed to right-hand circular polarized light. It might take several cycles of absorption and emission, but those happen very rapidly-- tens of nanoseconds-- so in a fraction of a millisecond you can move essentially all the atoms in a sample into the positive-angular-momentum state.

And if you use left-hand circular polarization, it goes the other way? Exactly. Left-hand light will inevitably drive the atoms into the negative-angular-momentum ground-state level. Either direction will work, depending on your choice of laser polarization.

And this gets you cooling... how? These states have the same energy, don't they? So what's the difference? They start out with the same energy, but remember, they're in a laser field where the polarization of the light changes as you move from one place to another. And that means the two levels are subject to a different light shift, depending on the polarization of the light.

Why is that? In a very loose way, you can think about it in terms of the optical pumping process. An atom in the negative-angular-momentum state sitting in right-hand circular light isn't going to stay in that state very long, so it doesn't interact with the light all that much, and feels a small light shift. Once it's in the positive-angular-momentum state, though, it stays there and interacts strongly with the light, feeling a big shift.

The opposite is true for left-hand circular polarization: in left-hand circular light, the negative-angular-momentum level feels a big shift, and the positive-angular-momentum state feels very little shift. And this is the key to Sisyphus cooling.

How does that work? Well, here's a cartoon of the process, drawn from my lecture slides for this stuff:

Sisyphus cooling.

Imagine you start in a region of right-hand circular polarization, with an atom in the positive-angular-momentum state. It feels a big light shift, lowering its energy. As it moves, though, it starts to leave the area of right-hand circular polarization, and the light shift decreases, so its internal energy goes up. That energy has to come from somewhere, so it slows down, as if it were rolling up a hill.

When it gets to the top of the "hill," then, it's lost some amount of energy (the exact amount depends on the intensity and detuning of the lasers). But the whole reason it's at the top of the hill is that the polarization of the light field has changed-- now it's not sitting in right-hand circular light, it's sitting in left-hand circular light. And a positive-angular-momentum atom doesn't last long in left-hand-circular light before it gets optically pumped to the negative-angular-momentum state.

Which puts it back in a place with a big light shift? Exactly. When it pumps to the negative-angular-momentum state, that state is light shifted down. Which means it's back at the "bottom" of the hill, but now it's moving slower than it was initially.

Doesn't it get back the energy that it lost? No, because it's carried off by the light-- the photon it emits in going from the excited state to the negative-angular-momentum ground state has a very slightly higher energy that exactly makes up the change in the light shift. So it lost energy climbing the hill, and then finds itself back at the bottom.

Thus, "sisyphus cooling." Exactly. The atom's predicament is exactly like the punishment meted out to Sisyphus in the afterlife, after he pissed the Greek gods off in some manner I don't recall-- he was condemned to push a giant rock up a hill, but every time he neared the top, the rock would slip away and roll back to the bottom, forcing him to start over.

It didn't pay to piss the Greek gods off. No, they had a sick sense of humor. It works out well for atomic physics, though, because this effect turns out to be an exceptionally efficient way of cooling the atoms down. You get Doppler cooling at the start, and once the atoms are fairly cold, enough that the light shift is roughly the same scale as their kinetic energy, the sisyphus effect becomes important, and cools the atoms down to temperatures well below what you expect from the simple theory.

And nobody expected any of this? I can't say I'm surprised, given the complexity... It's not quite true to say that none of this was expected-- people knew about optical pumping, and in fact, that's how they justified using the simple two-level theory for talking about laser cooling. They reasoned that the light would pump all of the atoms into the extreme angular momentum states in very short order, and once that happened, you really had only two levels to worry about, so the simple theory should be just fine.

What they didn't anticipate was the effect of the polarization gradients. But once they started using optical molasses beams with different polarizations, the gradients happen automatically, and you get sisyphus cooling. And thus, much lower temperatures than had been believed possible.

Pretty cool, if you'll pardon the inadvertent pun. Just one question, though: Why were they using optical molasses beams with different polarizations? Isn't that more work? Well, there were two reasons: one was to avoid making an intensity pattern-- if you use the same polarization for beams in opposite directions, you end up making a standing wave with spots where there's no light at all. Using different polarizations lets you make a uniform intensity field, and that's nicer to think about.

But there's another, technological, reason why you would use beams with different polarizations, but...

I know, I know, that's the next post in the series... Got it in one.

drorzel Thu, 08/08/2013 - 05:47

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