Quantum Control and Entanglement in a Strongly Interacting Spin Ensemble

这项研究将研究在绝对零度附近冷却的超冷原子气体的量子相变。相变在包括宇宙学、粒子物理学和凝聚态物质在内的许多物理领域中都扮演着重要的角色。水冻结成冰提供了一个熟悉的例子：当温度降到冰点以下时，水分子的运动在结晶时经历了相变。在宇宙学中，人们推测宇宙的大尺度结构是宇宙在大爆炸后不久通过相变(通过所谓的“希格斯机制”)冷却时形成的缺陷的遗迹(例如“宇宙弦”)。这项研究将探索在温标另一端的未知区域中的量子相变和相关现象，在开尔文温标上接近绝对零度(或在华氏温标上接近零下460度)。这些实验将使用超冷原子玻色-爱因斯坦凝聚(一种在极低温度下形成的物质的量子态)来探索相变，在相变中，相变的行为由量子效应而不是热效应决定。除了为多粒子系统的基础量子科学提供新的见解外，这些实验还可能应用于量子信息科学，以及开发用于惯性制导和重力和磁场测量的新型量子传感器。这项实验研究将研究玻色-爱因斯坦凝聚体中自旋-1原子的强相互作用系综，以探索临界点附近量子相变的本质，并研究系综非经典高度纠缠态的创建、控制和表征。研究使用了只包含一个自旋域的小型Rb-87原子玻色-爱因斯坦凝聚体，使得动态演化只发生在内部自旋自由度中。这些凝聚体的特点是哈密顿量具有可调的量子相变，允许探索自旋的铁磁和极(向列)基态。精确可解的哈密顿量与量子相变的结合，以及量子体系中所展示的动力学，为探索重要课题提供了独特的工具组合，包括对二阶量子相变的高精度研究，跨量子临界点的激发的探索，以及大规模纠缠态的产生。所有这些研究的一个共同主题是有限尺寸效应的作用，这些效应体现在系统的量子涨落中。这项研究将提供对许多物理领域重要的多粒子量子力学的基本原理的洞察，并将为未来探索量子多体自旋系统指明方向，包括跨越量子相变的热化和遍历性，哈密顿量子混沌和其他非线性现象的研究，以及有限温度效应。

This research will investigate quantum phase transitions using ultracold atomic gases cooled close to absolute zero temperature. Phase transitions play important roles in many areas of physics including cosmology, particle physics and condensed matter. The freezing of water to ice provides a familiar example: the motion of water molecules undergo a phase transition upon crystallization as the temperature falls below the freezing point. In cosmology, it is conjectured that the large scale structure of the universe is a vestige of defects (e.g. "cosmic strings") formed as the Universe cooled through a phase transition (via the so-called "Higgs mechanism") shortly after the Big Bang. This research will explore quantum phase transitions and associated phenomena in an unexplored regime at the opposite end of the temperature scale, close to absolute zero on the Kelvin temperature scale (or nearly 460 degrees below zero on the Fahrenheit temperature scale). The experiments will use ultracold atomic Bose-Einstein condensates (a quantum state of matter that forms at extremely low temperatures) to explore phase transitions in which the behavior of the transition is determined by quantum effects rather than thermal effects. In addition to providing new insight to the fundamental quantum science of many-particle systems, these experiments have potential applications to quantum information science and to the development of new quantum sensors for inertial guidance and measurement of gravity and magnetic fields. This experimental research will study strongly interacting ensembles of spin-1 atoms in a Bose-Einstein condensate to explore the nature of quantum phase transitions in the neighborhood of the critical point and to investigate creation, control and characterization of non-classical highly entangled states of the ensembles. The investigations use small rubidium-87 atomic Bose-Einstein condensates containing just a single spin domain, such that the dynamic evolution occurs only in the internal spin degrees of freedom. These condensates feature a well-characterized Hamiltonian with a tunable quantum phase transition that allow exploration of both ferromagnetic and polar (nematic) ground states of the spins. The combination of an exactly solvable Hamiltonian with a quantum phase transition together with demonstrated dynamics in the quantum regime provide a unique combination of tools to explore important topics including high precision studies of a second order quantum phase transitions, exploration of excitations across a quantum critical point, and the generation of massively entangled states. A common theme in all of these studies is the role of finite size effects that manifest in the quantum fluctuations of the system. This research will provide insight into fundamental principles of many-particle quantum mechanics that are important to many areas of physics and will point the way to future explorations of quantum many-body spin systems including thermalization and ergodicity crossing a quantum phase transition, investigations of Hamiltonian quantum chaos and other non-linear phenomena, and finite temperature effects.