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 (16 dimensional for cesium, with nuclear spin i=7/2). The methods of optimal/robust control from a Lie algebraic perspective are employed, making use of the intrinsic symmetries of the atomic problem, driven by physical fields. With such control it is possible to explore the connection between the dynamical generation of entanglement in a bipartite system (here electron/nuclear) and the emergent chaotic dynamics in the classical description 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 the entanglement that is generated between an atomic ensemble and a laser probe into a quadratic nonlinearity of the collective spin will be investigated. Such nonlinearity should allow for the production of highly squeezed spin states, with the possibility of creating collective 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 the ability to continuously monitor atomic correlation functions, and thus explore an open-quantum-system approach to quantum many-body systems. NATIONAL SCIENCE FOUNDATION Diary Note Proposal:0653599 PI Name:Deutsch, Ivan Printed from eJacket: 02/13/07 Page 1 of 1
