ERC FUNDED PROJECTS

We envisage a new generation of dynamic holographic laser tweezers and stretching tools with unprecedented spatial control of gradient and scattering light forces, to unravel functional mysteries of cell biology and genetics: Based on our recently developed, highly successful and widely recognized amplitude and phase shaping techniques with cascaded spatial light modulators (SLM), we will create new holographic optical manipulators consisting of a line-shaped trap with balanced net scattering forces and controllable local phase-gradients. Combining these line stretchers with spiral phase contrast imaging or nonlinear optical microscopy will allow quantitative study of functional shape changes. The novel tool is hugely more versatile than standard optical tweezers, since direction and magnitude of the scattering force can be designed to precisely follow the structure. In combination with conventional multi-spot traps the line stretcher acts as a sensitive and adaptable local force sensor. In collaboration with local experts we want to tackle hot topics in Genetics, e.g. search for force profile signatures in regions with Copy Number Variations. Possibly the approach may shed light on basic physical characteristics such as, for example, chromosomal fragility in Fra(X) syndrome, the most common monogenic cause of mental retardation. The new design intrinsically offers enhanced microscopic resolution, as SLM-synthesized apertures and waveforms can enlarge the number of spatial frequencies forming the image. Ultimately, nonlinear holography can be implemented, sending phase shaped wavefronts to target samples. This can, e.g., be used to push the sensitivity of nonlinear chemical imaging, or for controlled photo-activation of targeted regions in neurons.

1 987 428 €

Start date: 2010-05-01, End date: 2015-04-30

Quantum computers offer a fundamentally new way of information processing. Within the scope of this proposal, quantum information processing with an ion trap quantum computer will be investigated. With the new combination of cryogenic technology and ion traps for quantum computing we intend to build a quantum information processor with strings of up to 50 ions and with two-dimensional ion arrays for an investigation of deterministic many-particle entanglement. The cryogenic traps will be applied for quantum simulations, for fundamental investigations concerning large-scale entanglement and for precision measurements enhanced by quantum metrology techniques employing entangled particles.

2 200 000 €

Start date: 2008-12-01, End date: 2013-11-30

Antihydrogen is the simplest atom consisting entirely of antimatter. Since its counterpart hydrogen is one of the best studied atoms in physics, a comparison of antihydrogen and hydrogen offers one of the most sensitive tests of CPT symmetry. CPT, the successive application of charge conjugation, parity and time reversal transformation is a fundamental symmetry conserved in the standard model (SM) of particle physics as a consequence of a mathematical theorem. These conditions for this theorem to be fulfilled are not valid any more in extensions of the SM like string theory or quantum gravity. Furthermore, even a tiny violation of CPT symmetry at the time of the big bang could be a cause of the observed antimatter absence in the universe. Thus the observation of CPT violation might offer a first indication for the validity of string theory, and would have important cosmological consequences. This project proposes to measure the ground state hyperfine (HFS) splitting of antihydrogen (HBAR), which is known in hydrogen with relative precision of 10^–12. The experimental method pursued within the ASACUSA collaboration at CERN-AD consists in the formation of an antihydrogen beam and a measurement using a spin-flip cavity and a sextupole magnet as spin analyser like it was done initially for hydrogen. A major milestone was achieved in 2010 when antihydrogen was first synthesized by ASACUSA. In the first phase of this proposal, an antihydrogen beam will be produced and the HBAR-HFS will be measured to a precision of around 10^–7 using a single microwave cavity. In a second phase, the Ramsey method of separated oscillatory fields will be used to increase the precision further. In parallel methods will be developed towards trapping and laser cooling the antihydrogen atoms. Letting the cooled antihydrogen escape in a field free region and perform microwave spectroscopy offers the ultimate precision achievable to measure the HBAR-HFS and one of the most sensitive tests of CPT.

2 599 900 €

Start date: 2012-03-01, End date: 2017-02-28

The Nazi system was not amoralism in the classical textbook sense but a specific, though contorted normative order. The basic argument was that political emergency conditions made it necessary to replace the unstable liberal-democratic framework of the Weimar Republic by a 'new source of law : the authority and political will of the Führer. The claim to correctly interpret the Führer s will and intentions became the new foundation of legitimate political action . Consequently emergency decrees, political initiatives, and party agitation replaced the rule of law. The Nazis worked, however, with a highly moralized conception of social reality, based on perverted notions of duty, honor, loyalty, fidelity, and sincerity. The Nazi regime provided people with justifications of policies and measures that for many followers amounted to a 'meaningful story . They managed to set a normative framework within which even fulfilling killing orders 'made sense . A perverted model of practical reasoning was propagated by the highest authorities according to which immediate reactions of resistance and revulsion counted as 'natural temptations' which had to be overcome. The aim of the project is to: - provide a detailed account of the normative order of the Nazi system and the transformations of the key political and legal institutions that it brought about; - analyze in detail the distorted notions of duty, obedience, and decency and the corresponding self-conceptions the Nazi regime encouraged; - explore the implications of our findings for the following broader questions: * How should we assess conceptions of normativity under non-ideal conditions? * What is the relationship between legality and legitimacy under non-ideal conditions? * What exactly are the standards for acting morally under non-ideal conditions?

1 261 004 €

Start date: 2010-07-01, End date: 2015-06-30

The proposal addresses some of the most pressing topics in optimal control of partial differential equations (PDEs): Non-smooth, non-convex optimal control and computational techniques for feedback control. These two topics will be applied to the large scale optimal control problems for the bidomain equations, which are the established model to describe the electrical activity of the heart. Due to their rich dynamical systems behavior these systems are particularly challenging. The use of non-smooth functionals is of great practical relevance in many diverse situations. They promote sparsity, and provide a perfect formulation for switching and multi-bang controls, and for the optimal actuator location problem. For inverse problems the case $L^{p}$ with $p\in (0,1)$ is of special statistical importance, and $L^0$ can be the basis of a new formulation for topology optimization problems. But lack of Lipschitz continuity and of convexity are significant obstacles which can only be overcome by the development of new analytical and numerical concepts. The new algorithmic concepts will also be applicable to important non-smooth problems in continuum mechanics, as for instance the quasi-static evolution of fractures. Closed loop control is of paramount importance due to its {\bf robustness} against system perturbations. Nevertheless, numerical realization of optimal feedback strategies for nonlinear PDEs has barely been touched since the curse of dimensionality makes direct numerical treatment of the Hamilton-Jacobi-Bellman equation unfeasible. We shall therefore develop and analyze suboptimal strategies based on model reduction and interpolation techniques, and on model-predictive control. The availability of boundary and near-to-the boundary measurements together with dynamic observer techniques will allow to test the proposed methods to obtain suboptimal feedback controls for the bidomain equations.

1 678 325 €

Start date: 2016-01-01, End date: 2020-12-31

One of the most important developments in modern physics was the recent emergence of quantum information science, which by its very nature is broadly multidisciplinary. It was started by investigations of the foundations of quantum mechanics, and fundamental quantum concepts, most notably, entanglement, play a key role. We are now at an historic moment where a major qualitative step, both in developing a new technology and applying it to new fundamental questions, can be made. In this proposal, we aim to combine the investigation of fundamental questions with the development of micro-optics technology to reach a new level of both quantum information experiments and fundamental tests of quantum mechanics. We propose to utilize the advanced development of micro-optics to build novel integrated quantum optics photonic chips. High quality micro-optics will allow precise control over many properties, including birefringence, dispersion, periodicity, and even absorptive properties. We will combine this with novel highly efficient detectors, hopefully, in the long run, also integrated into the same microchips. By their very nature, the new multi-mode devices will make new higher-dimensional regions of Hilbert space and new types of multi-photon entanglement accessible to experiment. Such devices will enable many new fundamental investigations of quantum mechanics, such as, to give just one example, exploring quantum complementarity both between different numbers of photons and as a function of Hilbert space dimension with significant mathematical implications. Most importantly, we are convinced that many new ideas will arise throughout the project. The new integrated quantum optical chips will also be important in quantum computation, specifically with cluster states and similar complex quantum states. With these chips, we will realize multi-qubit procedures and algorithms and demonstrate the feasibility of all-optical quantum computation in realistic scenarios.

1 750 000 €

Start date: 2009-01-01, End date: 2013-12-31

"Large complex systems tend to develop universal patterns that often represent their essential characteristics. A pioneering vision of E. Wigner was that the distribution of the gaps between energy levels of complicated quantum systems depends only on the basic symmetry of the model and is otherwise independent of the physical details. This thesis has never been rigorously proved for any realistic physical system but experimental data and extensive numerics leave no doubt as to its correctness. Wigner also discovered that the statistics of gaps can be modelled by eigenvalues of large random matrices. Thus the natural questions, “How do energy levels behave?” and “What do eigenvalues of a typical large matrix look like?”, have surprisingly the same answer! This project will develop new tools to respond to the two main challenges that Wigner’s vision poses for mathematics. First, prove that a large class of natural systems exhibits universality. The simplest model is the random matrix itself, for which the original conjecture, posed almost fifty years ago, has recently been solved by the PI and coworkers. This breakthrough opens up the route to the universality for more realistic physical systems such as random band matrices, matrices with correlated entries and random Schrödinger operators. Second, eigenvalue statistics will be used to detect the basic dichotomy of disordered quantum systems, the Anderson metal-insulator transition. Third, describe the properties of the strongly correlated eigenvalues viewed as a point process. Although this process appears as ubiquitous in Nature as the Poisson process or the Brownian motion, we still know only very little about it. Due to the very strong correlations, the standard toolboxes of probability theory and statistical mechanics are not applicable. The main impact of the project is a conceptual understanding of spectral universality and the development of robust analytical tools to study strongly correlated systems."

1 754 717 €

Start date: 2014-03-01, End date: 2019-02-28

The recent financial crisis has brought to light the importance of correctly evaluating financial assets and their underlying risk. Any such valuation should be robust, i.e., should not be overly sensitive to the modelling assumptions. According to the Black--Scholes theory, which lies at the heart of most current valuation methods, the risk involved by a financial asset can be perfectly eliminated by pursuing a proper dynamic hedging strategy. Unfortunately, although formally elegant, this theory is too much of an idealization of the real world situation. The underlying model fails to be robust in two ways: the prices follow geometric Brownian motion, and transaction costs must be zero. The use of alternative models, e.g. based on fractional Brownian motion, was proposed more than 45 years ago by B.~Mandelbrot. The empirical findings give support to the use of such alternative models. Nevertheless, up to now these models could not be used to value financial assets, as they are not free of arbitrage. We propose an approach which makes it possible to value financial assets in an arbitrage free way, even in the framework of fractal models, by properly taking transaction costs into account. Our approach is based on utility theory. We also propose to control the risk of the related hedging strategies by imposing bounds in terms of risk measures. This allows for more realistic financial modelling with special emphasis on the aspect of the residual risk, remaining after hedging. From a mathematical point of view, our approach is based on the duality theory of infinite-dimensional optimization.

1 266 000 €

Start date: 2010-04-01, End date: 2015-03-31