Collaborative Research: Quantum Control of Qudits and Quantum Transport in Optical Lattics

这一NSF奖将支持开发控制和测量其行为受量子力学支配的物理系统的一般方法。作为一个具体的物理试验台，该项目将使用冷原子和光学晶格(用于捕获冷原子的干涉激光形成的空间周期性势垒)。该系统提供了对广泛的量子现象的访问，并被认为是量子计算等量子信息科学的领先平台之一。目前的目标是开发强大而灵活的控制工具来操作以原子基态(Qudits)的有限集(Qudits)编码的量子信息。通过将原子的状态与其在光学晶格中的位置相关联，可以控制原子在网格上的量子力学运动。如果原子-晶格系统要用于量子计算和凝聚态物理的量子模拟，对原子内部和运动量子态的同时量子控制将是必不可少的，这两者都是世界各地研究小组追求的重大挑战。当物理设备被用于执行现实世界的任务时，这个过程可以抽象地理解为系统响应外部命令(控制)通过一系列配置(状态)。在实践中，即使在存在错误和缺陷的情况下，设备的控制也必须准确可靠。即使对于由经典力学支配的系统来说，这也是一个不小的挑战，并在历史上催生了一门被称为控制科学的完整工程学科。现代纳米科学的进步正在推动技术进入量子领域，因此必须建立一个类似的新的量子控制领域。这一NSF奖将对量子控制和量子信息科学的知识基础做出重大贡献。值得注意的是，为冷原子和光学晶格平台开发的工具和技术将广泛适用，因为任何量子系统的控制设计都基于一套单一的数学原理，无论是原子、分子、光学还是凝聚态物质。研究的所有方面都将涉及研究生，并将在量子信息与控制中心(CQuIC)的框架内进行，CQuIC是一个新成立的合资企业，由新墨西哥大学和亚利桑那大学的首席研究人员参与。因此，该奖项将有助于培训未来量子控制和量子信息科学方面的科学家和研究人员。

This NSF award will support the development of general methods to control and measure physical systems whose behavior is governed by quantum mechanics. As a concrete physical testbed the project will use cold atoms and optical lattices (spatially periodic potential wells formed by interfering laser beams used to trap cold atoms). This system provides access to a broad range of quantum phenomena, and is considered one of the leading platforms for quantum information science such as quantum computation. The immediate goal is to develop robust and flexible control tools to manipulate quantum information encoded in finite sets of atomic ground states (qudits). By correlating the state of an atom with its position in an optical lattice, it becomes possible to control the quantum mechanical motion of atoms on a grid. Simultaneous quantum control of the internal and motional quantum states of atoms will be essential if the atom-lattice system is to be used for quantum computation and quantum simulation of condensed-matter physics, both of which are grand challenges pursued by research groups across the world.When physical devices are used to perform real world tasks, the process can be understood abstractly in terms of a system moving through a sequence of configurations (states) in response to external commands (controls). In practice, control of the device must be accurate and reliable even in the presence of errors and imperfections. This is a non-trivial challenge even for systems governed by classical mechanics, and has historically given rise to an entire engineering discipline known as Control Science. Modern advances in nanoscience is pushing technology into the quantum realm, and an analogous new field of Quantum Control must therefore be established. This NSF award will contribute substantially to the knowledge base of Quantum Control and Quantum Information Science. Notably, the tools and techniques developed for the cold atoms and optical lattice platform will be broadly applicable because a single set of mathematical principles underlie the design of controls for any quantum system, be it atomic, molecular, optical or condensed matter. All aspects of the research will involve graduate students, and will occur within the framework of the Center for Quantum Information and Control (CQuIC), a newly established joint venture involving principal investigators at the University of New Mexico and the University of Arizona. The award will thus contribute to the training of future scientists and researchers in Quantum Control and Quantum Information Science.