Energy Functionals for Manifold-valued Mappings and Their Properties

This technical report is merely an extended version of the appendix of Steinke et.al. "Manifold-valued Thin-Plate Splines with Applications in Computer Graphics" (2008) with complete proofs, which had to be omitted due to space restrictions. This technical report requires a basic knowledge of differential geometry. However, apart from that requirement the technical report is self-contained

The role of quantum fluctuations in the optomechanical properties of a Bose-Einstein condensate in a ring cavity

We analyze a detailed model of a Bose-Einstein condensate trapped in a ring optical resonator and contrast its classical and quantum properties to those of a Fabry-P{\'e}rot geometry. The inclusion of two counter-propagating light fields and three matter field modes leads to important differences between the two situations. Specifically, we identify an experimentally realizable region where the system's behavior differs strongly from that of a BEC in a Fabry-P\'{e}rot cavity, and also where quantum corrections become significant. The classical dynamics are rich, and near bifurcation points in the mean-field classical system, the quantum fluctuations have a major impact on the system's dynamics.Comment: 11 pages, 11 figures, submitted to PR

Quantum measurement backaction from a BEC coupled to a mechanical oscillator

We study theoretically the dynamics of a a hybrid optomechanical system consisting of a macroscopic mechanical membrane magnetically coupled to a spinor Bose-Einstein condensate via a nanomagnet attached at the membrane center. We demonstrate that this coupling permits us to monitor indirectly the center-of-mass position of the membrane via measurements of the spin of the condensed atoms. These measurements normally induce a significant backaction on the membrane motion, which we quantify for the cases of thermal and coherent initial states of the membrane. We discuss the possibility of measuring that quantum backaction via repeated measurements. We also investigate the potential to generate non-classical states of the membrane, in particular Schrodinger cat states, via such repeated measurements.Comment: 14 pages, 4 figures. Submitted to PR

Generation of mechanical squeezing via magnetic dipoles on cantilevers

A scheme to squeeze the center-of-mass motional quadratures of a quantum mechanical oscillator below its standard quantum limit is proposed and analyzed theoretically. It relies on the dipole-dipole coupling between a magnetic dipole mounted on the tip of a cantilever to equally oriented dipoles located on a mesoscopic tuning fork. We also investigate the influence of several sources of noise on the achievable squeezing, including classical noise in the driving fork and the clamping noise in the oscillator. A detection of the state of the cantilever based on state transfer to a light field is considered. We investigate possible limitations of that scheme.Comment: 11 pages, 11 figures, submitted to PR

Rotated stripe order and its competition with superconductivity in La1.88_{1.88}Sr0.12_{0.12}CuO4_4

We report the observation of a bulk charge modulation in La$_{1.88}$Sr$_{0.12}$CuO$_4$ (LSCO) with a characteristic in-plane wave-vector of (0.236, $\pm \delta$), with $\delta$=0.011 r.l.u. The transverse shift of the ordering wave-vector indicates the presence of rotated charge-stripe ordering, demonstrating that the charge ordering is not pinned to the Cu-O bond direction. On cooling through the superconducting transition, we find an abrupt change in the growth of the charge correlations and a suppression of the charge order parameter indicating competition between the two orderings. Orthorhombic LSCO thus helps bridge the apparent disparities between the behavior previously observed in the tetragonal "214" cuprates and the orthorhombic yttrium and bismuth-based cuprates and thus lends strong support to the idea that there is a common motif to charge order in all cuprate families.Comment: 6 pages, 4 figue

Laser and electron deflection from transverse asymmetries in laser-plasma accelerators.

We report on the deflection of laser pulses and accelerated electrons in a laser-plasma accelerator (LPA) by the effects of laser pulse front tilt and transverse density gradients. Asymmetry in the plasma index of refraction leads to laser steering, which can be due to a density gradient or spatiotemporal coupling of the laser pulse. The transverse forces from the skewed plasma wave can also lead to electron deflection relative to the laser. Quantitative models are proposed for both the laser and electron steering, which are confirmed by particle-in-cell simulations. Experiments with the BELLA Petawatt Laser are presented which show controllable 0.1-1 mrad laser and electron beam deflection from laser pulse front tilt. This has potential applications for electron beam pointing control, which is of paramount importance for LPA applications

Identification of Seismo-Volcanic Regimes at Whakaari/White Island (New Zealand) Via Systematic Tuning of an Unsupervised Classifier

We present an algorithm based on Self-Organizing Maps (SOM) and k-means clustering to recognize patterns in a continuous 12.5-year tremor time series recorded at Whakaari/White Island volcano, New Zealand (hereafter referred to as Whakaari). The approach is extendable to a variety of volcanic settings through systematic tuning of the classifier. Hyperparameters are evaluated by statistical means, yielding a combination of “ideal” SOM parameters for the given data set. Extending from this, we applied a Kernel Density Estimation approach to automatically detect changes within the observed seismicity. We categorize the Whakaari seismic time series into regimes representing distinct volcano-seismic states during recent unrest episodes at Whakaari (2012/2013, 2016, and 2019). There is a clear separation in classification results between background regimes and those representing elevated levels of unrest. Onset of unrest is detected by the classifier 6 weeks before the August 2012 eruption, and ca. 3.5 months before the December 2019 eruption, respectively. Regime changes are corroborated by changes in commonly monitored tremor proxies as well as with reported volcanic activity. The regimes are hypothesized to represent diverse mechanisms including: system pressurization and depressurization, degassing, and elevated surface activity. Labeling these regimes improves visualization of the 2012/2013 and 2019 unrest and eruptive episodes. The pre-eruptive 2016 unrest showed a contrasting shape and nature of seismic regimes, suggesting differing onset and driving processes. The 2016 episode is proposed to result from rapid destabilization of the shallow hydrothermal system, while rising magmatic gases from new injections of magma better explain the 2012/2013 and 2019 episodes