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.