Interactions With and Between Rydberg Atoms

气体中典型的原子和分子结构紧凑，除了在实验室中施加的最强的电场和磁场外，几乎不受其他任何物质的影响，而且它们彼此之间几乎不相互作用，除非在彼此相距很近的极少数情况下。使用简单的激光，原子或分子中的一个电子可以获得如此多的能量，以至于它几乎没有被原子或分子束缚。具有这种弱束缚电子的原子被称为里德堡原子，以约翰内斯·里德堡的名字命名，他给出了允许能量的数学描述。因为电子与原子或分子的结合很弱，所以它的性质可以用容易接近的小场来控制。此外，两个或多个里德伯原子之间的相互作用比通常的大数百万倍，这即使对稀释的气体也会产生有趣的原子-原子效应。该项目的主要技术目标是计算单个里德伯原子在静电或磁场或激光场中的性质，并计算许多相互作用的里德伯原子的性质。在过去的十年里，有越来越多的实验小组研究里德伯原子或分子和场的不同排列。该项目的一个总体目标是提供对实验结果的理解和/或提出值得研究的新安排。在不同领域研究里德伯原子的原因是，这个量子系统几乎完全受外部控制，因此有可能了解相互作用的哪些特性控制着能量和/或粒子在封闭系统内的运动。研究许多相互作用的里德伯原子也有类似的原因：能量在纯量子中的流动是一个基本问题，值得在不同情况下进行研究。最后，有几个建议使用里德伯原子作为量子计算机和/或非线性光学器件的组件。因此，使用最先进的计算技术进行的研究有助于了解这些建议的可行性。本项目将研究几种情形，在这些情形中，里德伯原子的电子特性被夸大为主要的共同特征。对于由暴露在强场中的单个里德伯原子以及通过其大电偶极矩相互作用的许多里德伯原子组成的系统，将进行计算。对于所有的系统，该小组将在计算中使用完全量子或量子和经典方法的混合方法。该项目的主要长期目标是开发理论和计算工具，使复杂量子现象的定量描述成为可能。所提出的计算涉及高激发态，其中波函数的许多节点允许复杂现象，或涉及许多体系统，其中粒子之间的相关性导致非平凡动力学。在基本层面上，这个目标是几乎所有原子理论建议的基本目标。因此，从这些研究中吸取的教训可能会引起广泛的兴趣。此外，了解这些系统可以允许对复杂状态和许多身体系统进行实验控制。有几个项目研究单个里德伯原子在暴露于强场时的行为。第一种情况是当原子暴露于瓶束阱中产生的结构势时；当原子核偏离中心时，这个势与原子核几乎没有对称性，所以几乎所有的态都混合在一起。第二种情况是理解量子摩擦（以自发发射的形式）在驱动量子系统中所起的作用；这个系统很有趣，因为经典动力学导致振荡器锁定在驱动器上。经典运动不会在o点之外衰减，因此，即使存在“摩擦”，也可以永远保持高能量。涉及两个或多个相互作用的里德伯原子的项目侧重于该系统的不同方面，但调用类似的计算工具和理论思想。一个项目是研究一个原子由于里德堡-里德堡相互作用而受到的冲击，特别是对于封闭系统。由于原子之间的相互作用能量有限，这一问题可能会对量子计算方案产生影响。另一个项目是研究里德伯气体中的安德森局域化：原子位置的随机性转化为激发跳跃幅度的随机性。我们的目标是了解跳跃幅度的1/R3依赖性如何影响安德森局域化的基本特性。另一个项目是了解里德伯气体中近场和远场偶极子-偶极子相互作用的作用。通过系统地改变参与偶极-偶极相互作用的状态类型，可以将系统从主要的近场（具有大主量子数的状态）调整到远场（具有小主量子数的状态）。最后，计算沿外电场排列的具有大电偶极矩的两个里德伯原子之间的相互作用以及它如何影响原子的相对运动。这将研究是否有可能以快速的、随时间变化的方式改变电场的方向，从而使原子形成一个动态稳定的分子。

Typical atoms and molecules in a gas are compact and nearly impervious to all but the strongest electric and magnetic fields that can be applied in a laboratory, and they hardly interact with each other except for the rare cases when they pass within tiny distances of each other. Using simple lasers, one of the electrons in an atom or molecule can acquire so much energy that it is only barely bound to the atom or molecule. An atom with such a weakly bound electron is called a Rydberg atom after Johannes Rydberg who gave a mathematical description of the allowed energies. Because the electron is weakly attached to the atom or molecule, its properties can be controlled using modest fields that are easily accessible. Also, the interaction between two or more Rydberg atoms is millions of times larger than is usual which gives interesting atom-atom effects even for a dilute gas.The main technical goal of this project is to calculate the properties of a single Rydberg atom in static electric or magnetic fields or in laser fields and to calculate the properties of many interacting Rydberg atoms. Within the past decade, there have been an increasing number of experimental groups investigating different arrangements of Rydberg atoms or molecules and fields. One of the general goals of this project is to provide understanding of the experimental results and/or to propose new arrangements worth studying. The reason for investigating a Rydberg atom in different fields is that there is nearly full external control of this quantum system so that it is possible to learn what properties of the interaction control how energy and/or particles move within a closed system. There is a similar reason for studying many interacting Rydberg atoms: the flow of energy through a purely quantum is a fundamental question and is worth studying in different situations. Lastly, there have been several proposals to use Rydberg atoms as components in quantum computers and/or as non-linear optical devices. Thus, studies which use state-of-the-art computational techniques could aid in the understanding of the feasibility of these proposals.This project will investigate several situations where the exaggerated electronic properties of Rydberg atoms are the main common feature. Calculations for systems that consist of a single Rydberg atom exposed to strong fields as well as many Rydberg atoms that interact through their large electric dipole moments will be performed. For all of the systems, the group will use either fully quantum or a mixture of quantum and classical methods in the calculations. The main long term goal of this project is to develop theoretical and computational tools that allow the quantitative description of complex quantum phenomena. The calculations proposed involve highly excited states where the many nodes of the wave function allow for complex phenomena or involve many body systems where the correlations between particles lead to nontrivial dynamics. At a basic level, this goal is a fundamental goal of nearly all atomic theory proposals. Thus, the lessons learned in these studies could be of wide interest. Also, understanding these systems could allow for experimental control of complex states and many body systems.There are a couple of projects that investigate how a single Rydberg atom behaves when exposed to strong fields. The first situation is when an atom is exposed to the structured potential that arises in a bottle-beam trap; when the nucleus is off-center, this potential has little symmetry with respect to the nucleus so that nearly all states are mixed together. The second situation is to understand the role that quantum friction (in the form of spontaneous emission) plays in a driven quantum system; this system is interesting because the classical dynamics leads to the oscillator locking to the drive. The classical motion does not decay out of the O-point and, thus, can remain forever with high energy even though 'friction' is present. The projects involving two or more interacting Rydberg atoms focus on separate aspects of this system but invoke similar computational tools and theoretical ideas. One project is to study the kick an atom receives due to Rydberg-Rydberg interactions, especially for blockaded systems. This kick arises due to the finite interaction energy between the atoms and could have implications for quantum computation schemes. Another project is to study Anderson localization in a Rydberg gas: the randomness in the placement of atoms translates into a randomness in the hopping amplitude of an excitation. A goal is to understand how the 1/R3 dependence in the hopping amplitude affects the basic properties of Anderson localization. Another project is to understand the role that near-field versus far-field dipole-dipole interactions play within a Rydberg gas. By systematically varying the types of states participating in the dipole-dipole interaction, one can tune the system from predominantly near-field (states with large principle quantum number) to far-field (states with small principle quantum number). Lastly, calculations of the interaction between two Rydberg atoms with large electric dipole moments aligned along an external electric field and how it affects the relative motion of the atoms will be performed. This will investigate whether it is possible to vary the direction of the electric field in a rapid, time dependent manner so that the atoms form a dynamically stable molecule.