Toward an Ab-initio Understanding of Ultracold Boson Experiments in One Dimension

量子世界是激光和超导等罕见现象的来源，这些现象对社会产生了巨大的影响。量子现象本质上是脆弱的，很难观察和研究，更不用说解释了。自20世纪90年代中期观察到玻色-爱因斯坦凝聚以来，在真空室中被电磁场捕获并操纵的超冷气体（绝对温度接近零的气体）为探索量子世界提供了一个独特的窗口。当原子只允许在一个空间方向上运动时，用超冷气体进行的实验正在检验量子效应。这种降低的维度可以夸大“量子性”，并产生新的物质状态。该项目将开发理论模型来描述这些状态并研究它们的可观察属性。待开发的模型预计将有助于理解电子相互作用强烈的材料以及它们沿着某些空间方向的运动受到限制的材料；例如，在纳米尺度的电线中。这些系统的特性，与传统研究的无约束（三维）量子系统的特性不一致，可能对理解广泛的纳米器件至关重要。本理论研究将探讨平衡态和非平衡态量子气体中的现象。在平衡中，需要回答的一个问题是，二维光学晶格中的三维玻色-爱因斯坦凝聚体的绝热载荷是否会导致一维气体处于热平衡状态，或者是否需要广义吉布斯系综来描述它们。研究人员还将研究在一维气体中添加一个额外的弱晶格时产生的现象，以及实验实现的相关量子相。远离平衡，这个项目将探索一维气体在相互作用下的膨胀动力学，沿着膨胀方向有或没有光学晶格，以及诸如限制势强度或晶格深度等参数在时间上周期性调制的实验。另一个有待探讨的问题是，在原子远离平衡状态且相互作用强烈的实验中，带映射程序的结果。提出的研究将主要由两名研究生进行，他们将接受计算和多体量子物理方面的培训。PI将设计一门关于量子统计力学的高级研究生课程，并将通过在Hazleton One社区中心发表关于一般科学特别是物理学的演讲，为Hazleton集成项目（http://www.hazletonintegrationproject.com）做出贡献。

The quantum world is a source of uncommon phenomena, such as lasing and superconductivity, that have had tremendous impacts on society. Intrinsically fragile, quantum phenomena are difficult to observe and study, let alone explain. Since the observation of Bose-Einstein condensation in the mid-1990s, ultracold gases (gases at nearly zero absolute temperature) that are trapped and manipulated with electromagnetic fields in vacuum chambers have provided a unique window for the exploration of the quantum world. Experiments with ultracold gases are examining quantum effects when atoms are allowed to move only in one spatial direction. This reduced dimensionality can exaggerate "quantum-ness" and produce novel states of matter. This project will develop theoretical models to describe such states and study their observable properties. The models to be developed are expected to aid in the understanding of materials in which electrons interact strongly and in which their motion along some spacial direction is constrained; for example, in nano-scale wires. The properties of these systems, at odds with those of traditionally studied unconstrained (three-dimensional) quantum systems, might be essential to the understanding of a wide range of nano-devices. This theoretical research will explore phenomena in quantum gases in equilibrium and far from equilibrium. In equilibrium, one of the questions to be answered is whether the adiabatic loading of three-dimensional Bose-Einstein condensates in two-dimensional optical lattices results in one-dimensional gases that are in thermal equilibrium, or whether generalized Gibbs ensembles are needed to describe them. The researchers will also study phenomena which result when an additional weaker lattice is added along the one-dimensional gas, and the associated quantum phases that are realized experimentally. Far from equilibrium, this project will explore the expansion dynamics of one-dimensional gases in the presence of interactions, with or without an optical lattice along the expansion direction, as well as experiments in which parameters such as the strength of the confining potential or the lattice depth are periodically modulated in time. Another problem to be explored is the result of band-mapping procedures in experiments in which the atoms are far-from-equilibrium and interact strongly. The research proposed will be mostly carried out by two graduate students who will be trained in computational and many-body quantum physics. The PI will design an advanced graduate course on quantum statistical mechanics, and will contribute to the Hazleton Integration Project (http://www.hazletonintegrationproject.com) by giving talks at the Hazleton One Community Center about science in general and physics in particular.