Experimentally switching between liquid and solid phases?

Looking at Grochola's free energy path, I thought it was a nice computational technique.

The March 2004 issue of Physics Today has an article on controlling atoms and ions in optical traps (it's actually about using these for quantum information processing). On page 41, it describes putting the atoms in a optical lattice. The depth of the wells and the hopping matrix elements can be controlled by varying the intensity of the lasers creating the lattice.

This seems like one could experimentally switch between solid and liquid states without going through a phase transition.

There are some differences - I don't know if they are important or not. First, the experimental setup is a quantum system, Grochola's paper describes a classical system. Second, the confining potential is different. In the experimental setup, atoms are confined to any lattice site, but are not tethered to a particular lattice site.

The Physics Today article mentions a Mott insulator transition when the confining potential becomes strong enough. This transition seems due to the superfluid (quantum) nature of the liquid state. If the experiment were performed on a non-superfluid system, this transition would not happen ??

Update (3/16/2004): I forgot the final stage in the path - turning off the confining potential to get a stable solid state. I'm guessing the lattice spacing of the optical lattice is at least the laser wavelength or greater, so it's much larger than the lattice spacing of a normal solid. But some atoms can have their scattering length tuned - could it be made large enough to be comparable to the optical lattice spacing? In that case the atoms would behave as hard spheres (most importantly, there would likely not be enough attraction to keep the solid together), so an external potential would be required. Most of these setups seem to generate a harmonic confining potential (a box-like potential seems much harder to generate??), so the question is - what is the behavior of hard spheres in a harmonic potential?

For this system, there are two parameters - the number of particles and the strength of the external potential. I suspect there would be three regimes - one all liquid, one with a solid center surrounded by a liquid exterior, and one would be all solid. To take the thermodynamic (large N) limit, it seems that one would need to increase the particle number and decrease the external potential strength simultaneously to keep the central density or pressure constant (otherwise the pressure/density at the center would increase with added particles). Or maybe such a limit doesn't exist?