A discrete invitation to quantum filtering and feedback control

The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a novel field of application for stochastic estimation and control theory. In this expository paper we demonstrate estimation and feedback control of quantum mechanical systems in what is essentially a noncommutative version of the binomial model that is popular in mathematical finance. The model is extremely rich and allows a full development of the theory, while remaining completely within the setting of finite-dimensional Hilbert spaces (thus avoiding the technical complications of the continuous theory). We introduce discretized models of an atom in interaction with the electromagnetic field, obtain filtering equations for photon counting and homodyne detection, and solve a stochastic control problem using dynamic programming and Lyapunov function methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be found at http://minty.caltech.edu/papers.ph

On the Quantum Phase Operator for Coherent States

In papers by Lynch [Phys. Rev. A41, 2841 (1990)] and Gerry and Urbanski [Phys. Rev. A42, 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, B\"uchler and Lifkin [Phys. Lett. 49A, 119 (1974)] are in good agreement with the variance of the Pegg-Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase $\phi_0$ of the Pegg-Barnett phase operator. This off-set phase is replaced with the phase of a reference beam in an actual experiment and we show that several choices of such a relative phase can be fitted to the experimental data. We also discuss the Noh, Foug\`{e}res and Mandel [Phys.Rev. A46, 2840 (1992)] relative phase experiment in terms of the Pegg-Barnett phase taking post-selection conditions into account.Comment: 8 pages, 8 figures. Typographical errors and misprints have been corrected. The outline of the paper has also been changed. Physica Scripta (in press

Daily physical activity assessment: comparison between movement registration and doubly labeled water.

Daily physical activity assessment: comparison between movement registration and doubly labeled water. Bouten CV, Verboeket-van de Venne WP, Westerterp KR, Verduin M, Janssen JD. Department of Human Biology, University of Limburg, Maastricht, The Netherlands. [email protected] The use of movement registration for daily physical activity assessment was evaluated during a 7-day period in 30 free-living subjects. Body movement was registered with a Tracmor motion sensor consisting of a triaxial accelerometer and a data unit for on-line processing of accelerometer output over 1-min intervals. Average Tracmor output was correlated against four different energy estimates: 1) average daily metabolic rate (ADMR), determined with doubly labeled water; 2) ADMR-sleeping metabolic rate (SMR; determined in a respiration chamber); 3) (ADMR-SMR) per kilogram of body mass; and 4) the overall physical activity level (PAL = ADMR/SMR). The highest correlation was found for the relationship between Tracmor output and PAL (r = 0.58). After correction for Tracmor values arising from vibrations produced by transportation means, this correlation was improved to 0.73. There was no difference between Tracmor output and PAL in discriminating between overall activity levels with "low" (PAL 1.85) intensity. It is concluded that the Tracmor can be used in free-living subjects to distinguish among interindividual as well as intraindividual levels of daily physical activity

On the center of mass of Ising vectors

We show that the center of mass of Ising vectors that obey some simple constraints, is again an Ising vector.Comment: 8 pages, 3 figures, LaTeX; Claims in connection with disordered systems have been withdrawn; More detailed description of the simulations; Inset added to figure