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领域，与实验很少或没有联系。然而，在受限量子简并气体上的实验最近得到了一些可积系统的忠实的AMO实现。原子、分子和光学物理中独特的可积模型的新现象学相关性，开辟了一个新的研究方向的可能性，这是本提案的重点：冷稀释量子气体中可积性的实验表现。结果表明，在量子系统中存在非平凡的守恒量会导致系统平衡状态与热力学预测之间存在巨大的初始状态依赖差异。提出了一种新的热力学系综，并成功地进行了数值测试：在这种系综中，所有的运动积分都是平等参与的。此外，我们推测可积系统中的松弛动力学与一般系统有很大的不同：它不能简化为对少体碰撞的分析，而是实质上的多体效应。总的来说，有人认为可积量子气体的动力学和热力学性质与通常的如此不同，以至于它们完全符合量子物质的新状态。选择的研究对象包括深Mott区一维光学晶格中的玻色子，波导中自旋为0的玻色和自旋为1/2的费米气体，以及已经在实验中实现的二维谐波捕获玻色凝聚体。动量分布和化学成分是对可积性影响最敏感的实验观测值。

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.