We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations, and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial state for the condensate, and compare results to those for single-mode models.

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We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer-based control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a particle in a double-well potential.

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that is analyzed by dual-inlet isotope ratio mass spectrometry (IRMS). We describe a new laser spectroscopy instrument for highprecision 17 O measurements. The new instrument uses cavity ring-down spectroscopy (CRDS) with laser-currenttuned cavity resonance to achieve reduced measurement drift compared with previous-generation instruments. Liquid water and water-vapor samples can be analyzed with a better than 8 per meg precision for 17 O using integration times of less than 30 min. Calibration with respect to accepted water standards demonstrates that both the precision and the accuracy of 17 O are competitive with conventional IRMS methods. The new instrument also achieves simultaneous analysis of δ 18 O, δ 17 O and δD with precision of < 0.03 ‰, < 0.02 and < 0.2 ‰, respectively, based on repeated calibrated measurements.