Empirical Manifestations of Integrability in Cold Quantum Gases

冷量子气体可积性的经验表现

• 批准号: 0621703
• 负责人: Maxim Olchanyi
• 金额: $ 17.62万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2007-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0621703&HistoricalAwards=false
• 关键词: Empirical; Manifestations; Integrability; Cold; Quantum

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.

传统上可集成的量子多体系统属于数学物理域，与实验几乎没有联系。然而，对限制量子定位气体的实验最近对许多可集成的系统产生了忠实的AMO实现。原子，分子和光学物理独有的可集成模型的新现象学相关性打开了这项提案重点的新研究方向的可能性：冷稀量量子气体中的可整合性的实验表现。热力学。建议并成功地测试了一个新的热力学合奏：所有运动的积分都在相等的基础上参与。furthermore，可集成系统中的放松动力学猜想与通用构成非常不同：不能将其降低到几乎没有身体碰撞的分析中，但实际上是多种身体的效应。 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已经已经实现了实验性实现的。Momentum分布和化学组成被认为是对可合然效果敏感的最简单的实验性观察力。