Actually, people are all the time now going the other direction (or proposing to): they use cold atoms to simulate setups from condensed matter. The general ide

Actually, people are all the time now going the other direction (or proposing to): they use cold atoms to simulate setups from condensed matter. The general idea is that you can use lasers to site the atoms on a lattice, and then tune the interactions between the atoms to get all sorts of physics. A quick Google Scholar search turns up http://www.nature.com/nature/journal/v415/n6867/abs/415039a.html http://www.nature.com/nature/journal/v415/n6867/abs/415039a.... , wherein Greiner et al. simulate the Hubbard model (it would appear---I don't have access to the paper at the moment. This is cool, because the Hubbard model is a simple and displays interesting phenomena, but understanding it is a hard problem. The Hamiltonian (that is to say, the energy) consists only of a kinetic energy plus an interaction between the spin up and spin down particles on the same site (e.g. if I have two spin up bosons and four spin down bosons, the interaction contribution to the energy is 8 U, where U is a constant parameter---the strength of the interaction.) Depending on this interaction strength U, the system might behave either like a conductor or an insulator. The problem is hard to deal with analytically (for reasons I can't say I understand) and, as I understand it, the space of possible states is so huge that the numerics become computationally intractible at about a lattice 5 sites x 5 sites x 5 sites. So being able to see the phase transition happen is very neat, and exactly what you expect from an "analog quantum computer": simulating with cold atoms a system that we can't really simulate with ordinary computers.