Crystal healing

Lest this blog turn into a one-trick pony, let me tell you what I did today that’s of a little different flavor.

I epoxied some stuff onto some other stuff. More importantly, I calculated a band structure.

This amazes me. Sure, all you squa^Wsolid-state types out there do this every day, over your cereal even, and (in some cases) just have it done for you by the undergrad, but I’m an AMO physicist. I haven’t calculated a band structure since I first made sweet love to the Kronig-Penney potential back in the warrens of LeConte and Campbell, guided by the two-who-are-one, Cohen and Tannoudji. But I’m doing AMO, and band structure is a big part of my life now. What gives? Am I moonlighting on the side in some semiconductor fab trying to make a few bucks?

Hardly. See, solid-state physicists are interested in energy band structure because it’s a basic description of how electrons move in the periodic potential that is the crystal lattice in which they reside. An electron in a crystal moving about sees a nice orderly area of whoa-deep wells, and if we think about this quantum-mechanically, we realize that there’s a neat solution involving delocalized states known as Bloch wavefunctions, allowing the electron to do all the things we know and love, as long as it stays within energy bands whose shape depends on the particulars of the lattice in question.

Blah, blah, blah: electrons, crystals, Brillouin zones, reciprocal lattices– this stuff used to bore me to tears. I cared more about cleverly making bosons cold in a single macroscopic potential well rather than dealing with a Fermi gas of charged particles (how messy!) in a nanoscale lattice. Granted, I had a thesis to write, but I regret my single-mindedness. Now! Now I get to put cold neutral atoms into a lattice of my own design, for liberal interpretations of my and design. This is a big subfield of atomic physics these days, even– the construction and use of so-called optical lattices to explore quantum mechanics and (by construction) condensed-matter physics in a system that’s clean and customizable in ways that, um, Bardeen or…Onnes? could ever have imagined.

So what’s the secret? Neutral atoms have electrons in them, in some groundstate orbital. Alkalis (like rubidium) have a single valence electron, which gives them the nice characteristic of having decent electric and magnetic dipole moments. The magnetic dipole moment is useful for making magnetic traps, whereby you make a spatial minimum in magnetic field, which a weak-field-seeking atom sees as a bowl. The electric dipole moment is useful because it means the atom can be electrically polarized, meaning it’s happier in a region with intense electric fields, which conveniently can be made with lasers.

So that’s how we make a custom-built periodic potential for neutral atoms: we take a beam of focused laser light, reflect it upon itself to form a standing wave of constructive and destructive interference, and the atoms see regions of high intensity as valleys and dark regions as hills. Of course, this periodic potential is hundreds-of-nm scale instead of the nm-scale in, say, some sort of grotesque ruthenate, but that’s just a quibble. In my lab we have an analogue condensed-matter system with tunable tunnel couplings, temperature, band population, band structure, and even (thanks to BEC) phase coherence. And maybe one day, impurities that aren’t holes. More importantly, via time-of-flight imaging, we have access to the momentum distribution of the atoms in the lattice…but that’s a whole ‘nother bag of worms.

The setup I just told you about generates a 1-d sinusoidal potential, whose band structure isn’t rocket science. But with more and more beams you can do more and more Fourier components, and the can of tricks really opens up from there, in terms of interesting single-well geometries, and interesting band structures. The upshot: even though I have nothing but ultracold alkali vapor, a laser, and a few mirrors, I can justify the purchase of my own copy of Kittel.