Empirical Manifestations of Integrability in Cold Quantum Gases

可积量子多体系统传统上属于数学物理学的领域，与实验几乎没有联系。然而，最近的实验限制量子简并气体产生忠实的AMO实现的一些可积系统。可积模型的新现象学相关性，独特的原子，分子和光学物理学，开辟了一个新的研究方向的可能性，这是这个建议的重点：冷稀释量子气体中可积性的实验表现。结果表明，在量子系统中，系统的平衡态与热力学预测之间的初始状态依赖性差异。本文提出了一种新的热力学系综，并成功地进行了数值检验：在这种系综中，所有的运动积分都平等地参与.此外，可积系统中的弛豫动力学与一般的系统有很大的不同：它不能归结为对少体碰撞的分析，而是一种实质上的多体效应.总之，我们认为可积量子气体的动力学和热力学性质与通常的量子气体是如此不同，以至于它们完全符合量子物质的一种新状态。我们选择的研究对象包括在深Mott区的一维光学晶格中的玻色子，限制在波导中的自旋为0的玻色和自旋为1/2的费米气体，以及二维谐波囚禁的玻色凝聚体。动量分布和化学成分被认为是对可积性效应敏感的最简单的实验观测量。

Integrable quantum many-body systems traditionally belong to the domainof mathematical physics, with little or no connection to experiments. However, the experiments on confined quantum-degenerate gases has recently yielded faithful AMO realizations of a number of integrable systems. The new phenomenological relevance of integrable models, unique to atomic, molecular, and optical physics, opens up the possibility of a new research direction that is the focus of this proposal: the experimental manifestations of integrability in cold dilute quantum gases.It is shown that the presence of nontrivial conserved quantities in a quantum system leads to dramatic, initial-state-dependent discrepancy between the equilibrium state of the system and the predictions of thermodynamics. A new thermodynamic ensemble is suggested and successfully numerically tested: there all integrals of motion participate on an equal footing.Furthermore, the relaxation dynamics in an integrable system is conjectured to be very different from generic: it cannot be reduced to the analysis of few-body collisions, but is rather a substantially many-body effect. Overall, it is argued that the kinetic and thermodynamic properties of integrable quantum gases are so different from the usual, that they well-qualify for a new state of quantum matter.The objects of study chosen include bosons in one-dimensional optical lattices in the deep Mott regime, spin-0 Bose and spin-1/2 Fermi gases confined to waveguides, and two-dimensional harmonically trapped Bose condensates, all of which have been experimentally realized already.Momentum distribution and chemical composition are suggested as the simplest experimental observables sensitive to the effects of integrability.