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

True photo-counting statistics of multiple on-off detectors

We derive a closed photo-counting formula, including noise counts and a finite quantum efficiency, for photon number resolving detectors based on on-off detectors. It applies to detection schemes such as array detectors and multiplexing setups. The result renders it possible to compare the corresponding measured counting statistics with the true photon number statistics of arbitrary quantum states. The photo-counting formula is applied to the discrimination of photon numbers of Fock states, squeezed states, and odd coherent states. It is illustrated for coherent states that our formula is indispensable for the correct interpretation of quantum effects observed with such devices.Comment: 7 pages, 4 figure

Extension of the Measurement Capabilities of the Quadrupole Resonator

The Quadrupole Resonator, designed to measure the surface resistance of superconducting samples at 400 MHz has been refurbished. The accuracy of its RF-DC compensation measurement technique is tested by an independent method. It is shown that the device enables also measurements at 800 and 1200 MHz and is capable to probe the critical RF magnetic field. The electric and magnetic field configuration of the Quadrupole Resonator are dependent on the excited mode. It is shown how this can be used to distinguish between electric and magnetic losses.Comment: 6 pages, g figure

Abrupt longitudinal magnetic field changes in flaring active regions

We characterize the changes in the longitudinal photospheric magnetic field during 38 X-class and 39 M-class flares within $65^{\circ}$ of disk-center using 1-minute GONG magnetograms. In all 77 cases we identify at least one site in the flaring active region where clear, permanent, stepwise field changes occurred. The median duration of the field changes was about 15 minutes and was approximately equal for X-class and for M-class flares. The absolute values of the field changes ranged from the detection limit of $\sim\!\!10$~G to as high as $\sim\!\!450$~G in two exceptional cases. The median value was 69~G. Field changes were significantly stronger for X-class than for M-class flares and for limb flares than for disk-center flares. Longitudinal field changes less than 100~G tended to decrease longitudinal field strengths, both close to disk-center and close to the limb, while field changes greater than 100~G showed no such pattern. Likewise, longitudinal flux strengths tended to decrease during flares. Flux changes, particularly net flux changes near disk-center, correlated better than local field changes with GOES peak X-ray flux. The strongest longitudinal field and flux changes occurred in flares observed close to the limb. We estimate the change of Lorentz force associated with each flare and find that this is large enough in some cases to power seismic waves. We find that longitudinal field decreases would likely outnumber increases at all parts of the solar disk within $65^{\circ}$ of disk-center, as in our observations, if photospheric field tilts increase during flares as predicted by Hudson et al.Comment: Accepted to Ap

Quantum-state input-output relations for absorbing cavities

The quantized electromagnetic field inside and outside an absorbing high-$Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schr\"{o}dinger cat-like state is discussed.Comment: 12 pages, 5 eps figure