A paper of mine got posted recently (listed as 10/7, but it wasn't actually up last week; I first noticed it today). This paper, which appears in SIAM Journal of Applied Dynamical Systems, concerns Bose-Einstein condensates in optical superlattice potentials. (An alternative website if you don't have access to SIAM journals is here.)
To give a short-short explanation, BECs constitute a macroscopic quantum phenemon. Cool certain dilute Bose gases (like Na 23 and Rb 87) enough (to less than a microkelvin; I think some people can now get things to single-digit nanokelvin temperatures) and appropriately (evaporate cooling, like what happens with your coffee but on crack, is a key tool), and lots of particles condense into the ground state and you can see this beast via time-of-flight measurements (look in momentum space; see how fast particles move in a given amount of time). Animations and better intuitive explanations than I can give are available at the JILA BEC website. The existence of BECs were predicted in the 1920s (by Bose and Einstein; imagine that) and discovered experimentally in 1995 by Eric Cornell, Carl Wiemann, Wolfgang Ketterle (Jit Kee's Ph.D. advisor), and Randy Hulet. The first three of these guys got Nobeled in 2001. (Six years, of course, is an incredibly short turn-around time in this business. The impact of the discovery was clear from the beginning in this particular case.)
Normally, one puts BECs in harmonic potentials (traps), but there has been lots of work for the past few years in putting them in optical lattice potentials (spatially periodic potentials that are typically modeled by the functional form V_0cos(kx), although elliptical functions are useful for certain analyses). In a so-called "superlattice", one adds an extra lengthscale (or more) to the problem. In the models, this means the potential is the sum of two sinusoids. Experimentally, regular optical lattices are created by crossed lasers, and you can get superlattices by adjusting the angle between them. This has been reported in the literature once, but basically every group that can created regular optical lattices can also create superlattices.
One of the main things that my collaborators and I have been stressing (aka, harping on) is that superlattice potentials offer greatly increased flexibility in what one can do because of the extra lengthscale. The paper here discusses this in the context of spatially extended waves. We have some stuff going on right now (which we're revising today, actually) about controllable manipulation of localized solutions (solitary waves) using "dynamical" superlattice potentials. We're working on parametrically exciting BECs as well.
By the way, I apologize to any experimentalists in the audience for any butchering I did of those aspects.
Mason, you are actually very good at explaining things on simple terms. I tried to bring up BEC to high school students and your words in the first two paragraph are not that much more complicated than mine. Though I had a lot of animations to help. Any how. That's an interesting explanation of super latice. In digesting it, I got completely confused, and had to chat with my lab mate about it. -- My boss also works on "super-super-lattice", fun to say!-- and am now back in composure and eager to share: super-super-lattice is the periodic repeats of finite length cosines if you will. So I guess it's
ReplyDelete"periodic (periodic (quantum wells))".
-jing .... incidentally someone here in the department is nicknamed "super greg". but that may be besides the point. and I hear the new super man movie is good.
but, why? let's face it. BEC is so, like, 2001. -j.
ReplyDeleteThe mathematicians I know don't like the term superlattice, but it's not like I invented it. One person I know likes to change the terminology for things when he doesn't like the standard jargon, but that just adds to the confusion (immensely).
ReplyDeleteThere are animations on the JILA page to which I linked. The video that shows the condensate forming is especially useful. The extra lengthscale is something one can exploit mathematically. The reason I didn't want to define it in terms of cosines is that one could use other periodic functions (like elliptic functions), and there are times that that can be convenient for theoretical work.
Super Greg doesn't sound close to as good as Supermason, which I used once in e-mailing a student because her wording reminded me of some of the please for help on those old cartoons.
I didn't realize there was a new Superman movie. I don't think I ever saw any of the old ones.
Tell that to the cast of thousands writing PRLs as we speak... :)
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