Research

My research combines analytic and numerical approaches and seeks to incorporate system and control theoretic techniques and perspectives. A focus on quantitative treatment of experimentally accessible systems in optical and atomic physics accompanies consideration of more general or abstract problems. Some specific areas of research represented on my publications page are:

• Quantum information theory. Entanglement is at the bottom of many of the strange properties of quantum mechanics, such as violation of Bell inequalities or quantum teleportation. And yet for mixed states it's difficult even to say which states are entangled or which violate some Bell inequality and how to verify this physically. We have developed new tests for entanglement that generate observables that could in principle be measured to demonstrate the entanglement of any given state and have related these tests to the existence (or not) of certain kinds of local hidden variable theories. My work on these questions has applied ideas from the theory of a class of convex optimizations known as semidefinite programs. (with Pablo Parrilo, Federico Spedalieri, Barbara Terhal and David Schwab).
• Mechanical effects of light on atoms that are strongly coupled to optical cavities. These are relevant to recent experiments by the Kimble group at Caltech. In particular it was possible to develop simulations in quantitative agreement with an experiment that tracked the motion of single atoms in real time as they moved in the trapping potential provided by, on average, a single photon (with Christina Hood, Theresa Lynn, Jeff Kimble, Scott Parkins, Sze Tan and Dan Walls).
• Continuous measurement, state estimation and control of open quantum systems. A thorough investigation of quantum trajectories describing simple continuous quantum measurements (like position measurement of an oscillator) shows that quantum measurement theories are not always so different from their classical counterparts in control theory. Equally techniques from classical control theory can give us the insight necessary to design feedback controllers for quantum systems that depend on the entire history of the sensor output just like a classical servo does (with Kurt Jacobs, Hideo Mabuchi, Frank Verstraete, Sze Tan, Salman Habib, Howard Wiseman, Scott Parkins and Dan Walls).
• Precision measurements in quantum mechanics including adaptive phase measurements and force estimation through continuous position measurement (with JM Geremia, Frank Verstraete, Hideo Mabuchi, John Au, Mike Armen and John Stockton).