Estimating Electric Fields from Vector Magnetogram Sequences

Determining the electric field (E-field) distribution on the Sun's photosphere is essential for quantitative studies of how energy flows from the Sun's photosphere, through the corona, and into the heliosphere. This E-field also provides valuable input for data-driven models of the solar atmosphere and the Sun-Earth system. We show how Faraday's Law can be used with observed vector magnetogram time series to estimate the photospheric E-field, an ill-posed inversion problem. Our method uses a "poloidal-toroidal decomposition" (PTD) of the time derivative of the vector magnetic field. The PTD solutions are not unique; the gradient of a scalar potential can be added to the PTD E-field without affecting consistency with Faraday's Law. We present an iterative technique to determine a potential function consistent with ideal MHD evolution; but this E-field is also not a unique solution to Faraday's Law. Finally, we explore a variational approach that minimizes an energy functional to determine a unique E-field, similar to Longcope's "Minimum Energy Fit". The PTD technique, the iterative technique, and the variational technique are used to estimate E-fields from a pair of synthetic vector magnetograms taken from an MHD simulation; and these E-fields are compared with the simulation's known electric fields. These three techniques are then applied to a pair of vector magnetograms of solar active region NOAA AR8210, to demonstrate the methods with real data.Comment: 41 pages, 10 figure

Conditional quantum state engineering in repeated 2-photon down conversion

The U(1,1) and U(2) transformations realized by three-mode interaction in the respective parametric approximations are studied in conditional measurement, and the corresponding non-unitary transformation operators are derived. As an application, the preparation of single-mode quantum states using an optical feedback loop is discussed, with special emphasis of Fock state preparation. For that example, the influence of non-perfect detection and feedback is also considered.Comment: 17 pages, 4 figures, using a4.st

Conditional quantum-state transformation at a beam splitter

Using conditional measurement on a beam splitter, we study the transformation of the quantum state of the signal mode within the concept of two-port non-unitary transformation. Allowing for arbitrary quantum states of both the input reference mode and the output reference mode on which the measurement is performed, we show that the non-unitary transformation operator can be given as an $s$-ordered operator product, where the value of $s$ is entirely determined by the absolute value of the beam splitter reflectance (or transmittance). The formalism generalizes previously obtained results that can be recovered by simple specification of the non-unitary transformation operator. As an application, we consider the generation of Schr\"odinger-cat-like states. An extension to mixed states and imperfect detection is outlined.Comment: 7 Postscript figures, using Late