Interacting Atoms in Optical Lattices

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Usually, when particles or objects with different temperatures come into contact, they approach the same temperature as each other. After some time, there is no way to tell by looking at the particles or objects that they previously had different temperatures. That fact is such a fundamental part of our understanding of how the world works that it is called the "Zeroth Law of Thermodynamics". But it turns out that this is not always what happens. If all the particles interact in a certain special way, they retain a memory of earlier differences forever. That special way is called "integrability". It used to be considered a mathematical curiosity, something that couldn't happen in the real world. For classical particles, it was known in the 1960's that the Zeroth Law also does not hold for some systems even away from integrability. It was proven with equations and with computer simulations. But experiments had too many imperfections to demonstrate it in a lab. For particles whose motion is dominated by quantum mechanics, the answer of what happens away from integrability has not been understood with equations. Furthermore, even the best computers are not big or fast enough to give an answer. However, in the last few years, using very cold gases of atoms (a few billionths of a degree above absolute zero) confined by tubes of light so that they move only in one dimension, something very close to integrability has been demonstrated in the lab. These gases do not settle to a final temperature for as long as one can look at them, which is at least thousands of times longer than it takes similar gases to settle down in three dimensions. The question the group is now trying to answer is whether, with quantum mechanics, the Zeroth Law also doesn't hold when the integrability is not perfect. The answer to this question is important to the understanding of quantum mechanics, and it might make a big difference in the design of the growing number of devices (such as the most advanced prototype computers) that are based on collections of quantum particles. The group is attacking this question experimentally by taking 1D gases of ultra-cold atoms out of equilibrium, and then studying the steady state to which they evolve. The 1D systems are formed by 2D optical lattices. They will lift integrability in several qualitatively different ways. They can makes the systems slightly and controllably 2D by allowing weak tunneling between tubes in one transverse direction. Doing the same thing with tunneling in two transverse directions will make the system slightly more 3D. Integrability will also be lifted by adding a very weak axial lattice to the 1D gas. The effects of each of these non-integrable terms will be measured by observing the evolution of their 1D momentum distributions. The goal is to determine the range of validity of quantum statistical mechanics, and perhaps to point the way to new methods of preserving quantum information.