Tuesday, January 24, 2012

Cold atoms, optical lattices, and condensed matter physics

Over the last decade, since this experiment in particular, there has been rapidly growing interest in using optically trapped ultracold atoms, traditionally the tool of what people in the game call "atomic/molecular/optical" or "AMO" physics, to study condensed matter problems.  Using interfering laser beams, it is possible to make a spatially periodic pattern of optical intensity that acts like a spatially periodic potential energy.  Ultracold atoms (they have to be cold so that their kinetic energy is too low for them to fly out of the little potential wells) can be placed in this lattice in a controlled way.  The interactions between the atoms can be tuned using clever approaches, so that the interaction is so large that only one atom will like to sit in each little potential minimum.  It's also possible to tune the overlap of the potential wells to allow tunneling processes so that the atoms can move (virtually and in real space).  With other exceedingly clever modifications, it is even possible to use internal degrees of freedom of the atoms (e.g., nuclear spins), and to introduce effects equivalent to magnetic fields or spin-orbit coupling.

Condensed matter theorists love this stuff - you can actually implement the model problems they've been playing with for ages (e.g., the 2d Hubbard model on a square lattice), and all while maintaining exquisite tunability and control over the microscopic parameters.  Moreover, with spectroscopic techniques, you can probe these systems in real space (no need for diffraction experiments to see the periodic arrangement of atoms - just image them!), and pull out microscopic information (population and energy distributions) that is incredibly hard or impossible to get in solid materials.  These optical lattice systems are particularly great for examining nonequilibrium dynamics in microscopic detail.

This prompts a couple of questions.  First, is this condensed matter physics?  Yes, since the systems being modeled are condensed matter systems - that's how we denote theory, right?  (Empirically, some optical lattice results are now published in the condensed matter section of Phys Rev Letters, so there you go.)  Second, are there condensed matter systems that can't be modeled with these optical lattice methods?  Yes.  For one example, consider a material like VO2.  First, it's lattice structure is not something readily achievable in an optical lattice.  Second, this material undergoes a spontaneous structural change as a function of temperature, due to coupling between the electrons and the lattice.  In a cold atom system, you would somehow need the optical lattice itself to change depending on the positions of the atoms stored within it - I don't think anyone has figured out how to do such a thing.  I'm sure there are other examples, even in pure single-crystal systems.  Bottom line:  cold atom techniques for studying certain condensed matter problems are amazing and revolutionary, but there are going to be many CM systems that can't be accessed or modeled that way.


Sarang said...

Quick note that there has been some work on trying to realize optical lattices that are responsive to atomic motion: e.g., a paper we wrote a few years ago, http://www.nature.com/nphys/journal/v5/n11/full/nphys1403.html

Also: I believe it's now possible to realize virtually every 2D lattice structure. As an essentially random example I heard about yesterday: http://arxiv.org/abs/1109.1591

I do not know if three-dimensionality poses any really insuperable constraints, but doubt it.

Doug Natelson said...

Sarang - Thanks for the links. Regarding the Nature paper, that's clever, though in that case the atoms pick between two predetermined lattice configurations, rather than allowing the atoms+lattice to find a self-consistent configuration.

Concerning which lattices are achievable, it seems like one would have to use some kind of holography to generate truly complex lattices (e.g., the inverse spinel structure of Fe3O4, or the huge unit cell of Nd2Fe14B).

Peter Armitage said...

The guys are doing some remarkable things for sure. (Artificial spin-orbit coupling is just jaw dropping for instance).

But I wonder if ...

- degeneracy temperature will always be a issue? These gases are ultracold to you and me, but not to themselves necessarily. In the fermion version, T is always a substantial fraction of the Fermi temperature T_F. This is a constraint that electrons in solids don't have. Copper at room temperature is colder than the fermion versions of these systems.

- the parabolic potential will always be an issue? The gases are not confined in a box with flat walls. Real systems are typically in some sort of mixed regime with spatially vary profiles to some extent.

A real milestone will be crossed in this field when a state of matter is discovered in a cold atom system instead of just emulated. Here I mean discovered in the sense that superconductivity, the QHE, or spin-ice was discovered. Correct me if I am wrong, but I don't believe that has happened yet.

Sarang said...

Doug: it's not quite true that the cQED method (esp. the multimode version I linked to) is restricted to two predetermined configurations. And be that as it may, you do not need full self-consistency (which after all doesn't exist in the electron-phonon problem) to mimic structural distortions coupled to the motion of "electrons." While of course I agree that AMO systems have limitations that might be fundamental (heating, timescales, inhomogeneity, etc.), it is hard for me to see the space of realizable Hamiltonians as one of these.

Brian said...

Peter - You bring up good points on possible issues. I think the temperatures attainable will continue to be a problem. The method used to get to the coldest temperatures, evaporative cooling, fails for fermions well below the Fermi temperature due to Pauli blocking of collisions. So a new method will need to be developed to cool atoms further.

However, with respect to the underlying harmonic potential, that can be overcome. With the addition of another set of laser beams which repel atoms from their brightest region, you can cancel out the curvature. It may technically be challenging, but theoretically it should work.

Some guy said...

Pauli blocking is not a show stopper for cooling. One can cool sympathetically with other species, or even imagine immersing the fermions in a Bose condensate (Zoller proposal) which is itself continuously cooled, or any other number of things.

The point above about the relative temperature scales still stands however, but that's more of a limitation of how well you can practically thermally isolate the sample from the environment. Possibly bigger samples (and thus bigger k_F) can be made over time. In any event, such limitations simply lead people to investigate what's interesting and more readily accessible instead of what's less accessible (e.g., study unitary fermi gas, rather than packing up and going home because the critical temperature for a true BCS-limit superfluid is so low), which is what generally happens in science, right?

The fun things like artificial gauge fields / spin-orbit couplings do introduce a lot of heating, however, which does make things difficult if you want to play with such things.

And as for non-harmonic traps, there are certainly ways it can be done in principle, using time-varying potentials for example (i.e., "paint" an arbitrary potential with a laser beam by moving it faster than the relevant timescales of the atoms in the sample).

More exotic lattice structures and atom-state dependent lattices may look very difficult, but I would hate to speculate what will be possible in the coming years given the rate this stuff is moving now...