Quantum Control of Atomic Spins

该提案的两个基本主题是：(i)原子中耦合电子-核自旋系统的完全控制：该研究寻求在相当大的希尔伯特空间（铯为16维，核自旋i=7/2）上的快速和鲁棒控制。从李代数的角度出发，利用物理场驱动下原子问题的内在对称性，采用了最优/鲁棒控制方法。有了这样的控制，就有可能探索双粒子系统（这里是电子/核）中纠缠的动力学产生与耦合自由度经典描述中出现的混沌动力学之间的联系。（ii）原子系综集体自旋的量子控制：将研究一种基于反馈和量子擦除器的新协议，该协议将原子系综和激光探针之间产生的纠缠转化为集体自旋的二次非线性。这种非线性应该允许产生高度压缩的自旋态，并有可能产生具有非高斯统计的集体态。对多体动力学进行适当的研究，包括退相干和实验缺陷，对于更好地理解其运行机制是必要的。集体自旋的非经典态是原子之间具有量子相关性的态，因此为我们探索基本范式（如Lipkin-Meshkov-Glick模型）中的量子临界现象提供了一个窗口。特别感兴趣的是连续监测原子相关函数的能力，从而探索量子多体系统的开放量子系统方法。美国国家科学基金会（NATIONAL SCIENCE FOUNDATIONDiary）笔记提案：0653599 PI名称：Deutsch， ivanejacket: 02/13/07第1页

The two basic themes of the proposal are:(i) Complete control of the coupled electron-nuclear spin system in an atom:The research seeks rapid and robust control on a fairly large Hilbert space (16dimensional for cesium, with nuclear spin i=7/2). The methods of optimal/robust controlfrom a Lie algebraic perspective are employed, making use of the intrinsic symmetriesof the atomic problem, driven by physical fields. With such control it is possible toexplore the connection between the dynamical generation of entanglement in a bipartitesystem (here electron/nuclear) and the emergent chaotic dynamics in the classicaldescription of coupled degrees of freedom.(ii) Quantum control of the collective spin of the atomic ensemble:A new protocol based on feedback and a quantum-eraser that translates theentanglement that is generated between an atomic ensemble and a laser probe into aquadratic nonlinearity of the collective spin will be investigated. Such nonlinearity shouldallow for the production of highly squeezed spin states, with the possibility of creatingcollective states with non-Gaussian statistics. Proper studies of the many-body dynamics, including decoherence and experimental imperfections are necessary to better understand the operating regimes. The nonclassical states of the collective spin are those with quantum correlations between atoms, and thus provide us with a window to explore quantum critical phenomena in basic paradigms such as the Lipkin-Meshkov-Glick model. Of particular interest is theability to continuously monitor atomic correlation functions, and thus explore an open-quantum-system approach to quantum many-body systems.NATIONAL SCIENCE FOUNDATIONDiary NoteProposal:0653599 PI Name:Deutsch, IvanPrinted from eJacket: 02/13/07 Page 1 of 1