Continuous Measurement of Atomic Motion

Quantum mechanics is fundamentally a theory of measurement, and recently a paradigm in quantum optics has arisen for describing the \textit{continuous} measurement of quantum systems. Interesting phenomena can happen in continuously observed systems, due to the interplay of the dynamical evolution and the measurement process. In particular, the evolution of a quantum system under a continuous measurement process is both \textit{nonlinear} and \textit{stochastic}. I will describe our interests in continuous measurements of atomic motion, especially in applying continuous measurements to realizing quantum feedback control of atomic motion and to understanding the quantum--classical transition. I will also describe our experimental progress towards studying these systems. Finally, I will end with a model of a continuous measurement of the position of an atom that operates via the imaging of scattered laser light---a ``continuous Heisenberg microscope''---that has a surprising result: the information gained via the measurement in an intuitively ``good'' setup is much less that you would expect by considering the \textit{efficiency} of the measurement.