Interacting Atoms in Optical Lattices

通常，当具有不同温度的粒子或物体接触时，它们彼此接近相同的温度。一段时间后，没有办法通过观察粒子或物体来判断它们以前具有不同的温度。这个事实是我们理解世界如何运作的一个基本部分，它被称为“热力学第零定律”。但事实证明，这并不总是发生的事情。如果所有的粒子都以某种特殊的方式相互作用，那么它们就永远保留着对早期差异的记忆。这种特殊的方式被称为“可积性”。它曾经被认为是一种数学好奇心，在真实的世界中不可能发生的事情。对于经典粒子，在20世纪60年代就已经知道，第零定律对某些系统甚至远离可积性也不成立。这是用方程和计算机模拟证明的。但是实验有太多的不完善之处，无法在实验室中证明。对于那些运动受量子力学支配的粒子来说，在可积性之外会发生什么的答案还没有用方程来理解。此外，即使是最好的计算机也不够大或不够快，无法给出答案。然而，在过去的几年里，使用非常冷的原子气体（比绝对零度高几十亿分之一度），被光管限制，使它们只能在一维中运动，在实验室中已经证明了非常接近可积性的东西。这些气体不会在人们可以看到的时间内达到最终温度，这至少比类似气体在三维空间中稳定下来所需的时间长数千倍。该小组现在试图回答的问题是，在量子力学中，当可积性不完美时，第零定律是否也不成立。这个问题的答案对于理解量子力学很重要，而且它可能会对越来越多的基于量子粒子集合的设备（例如最先进的原型计算机）的设计产生很大的影响。该小组正在通过实验解决这个问题，方法是将超冷原子的一维气体从平衡状态中取出，然后研究它们演化到的稳定状态。一维光学系统由二维光学晶格构成。它们将以几种不同的方式提升可积性。它们可以通过允许在一个横向方向上的管之间的弱隧穿来使系统轻微且可控地二维化。在两个横向方向上做同样的事情，将使系统稍微更三维。通过在一维气体中加入一个非常弱的轴向晶格，也可以提高可积性。这些不可积项中的每一项的影响将通过观察它们的一维动量分布的演变来测量。其目标是确定量子统计力学的有效性范围，并可能为保存量子信息的新方法指明方向。

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.