## Publications

 Positivity of linear maps under tensor powers M, Alexander, Reeb, David and M. Wolf, Michael 2015 Abstract: We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n∈\mathbbN there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions we reduce the existence question of such non-trivial "tensor-stable positive maps" to a one-parameter family of maps and show that an affirmative answer would imply the existence of NPPT bound entanglement. As an application we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We furthermore show that the latter is an upper bound even for the LOCC-assisted quantum capacity, and that moreover it is a strong converse rate for this task. Linear and Non-linear Response of Lithographically Defined Plasmonic Nanoantennas Schraml, K., Kaniber, M., Bartl, J., Glashagen, G., Regler, A., Campbell, T. and J. Finley, J. Proceedings of SPIE 9371, 93711D (2015) 2015 Abstract: We present numerical studies, nano-fabrication and optical characterization of bowtie nanoantennas demonstrating their superior performance with respect to the electric field enhancement as compared to other Au nanoparticle shapes. For optimized parameters, we found mean intensity enhancement factors >2300x in the feed-gap of the antenna, decreasing to 1300x when introducing a 5nm titanium adhesion layer. Using electron beam lithography we fabricated gold bowties on various substrates with feed-gaps and tip radii as small as 10nm. In polarization resolved measurement we experimentally observed a blue shift of the surface plasmon resonance from 1.72eV to 1.35eV combined with a strong modification of the electric field enhancement in the feed-gap. Under excitation with a 100fs pulsed laser source, we observed non-linear light emission arising from two-photon photoluminescence and second harmonic generation from the gold. The bowtie nanoantenna shows a high potential for outstanding conversion efficiencies and the enhancement of other optical effects which could be exploited in future nanophotonic devices. Observation of many-body localization of interacting fermions in a quasi-random optical lattice Schreiber, Michael, S. Hodgman, Sean, Bordia, Pranjal, P. L, Henrik, H. Fischer, Mark, Vosk, Ronen, Altman, Ehud, Schneider, Ulrich and Bloch, Immanuel 2015 Abstract: We experimentally observe many-body localization of interacting fermions in a one-dimensional quasi-random optical lattice. We identify the many-body localization transition through the relaxation dynamics of an initially-prepared charge density wave. For sufficiently weak disorder the time evolution appears ergodic and thermalizing, erasing all remnants of the initial order. In contrast, above a critical disorder strength a significant portion of the initial ordering persists, thereby serving as an effective order parameter for localization. The stationary density wave order and the critical disorder value show a distinctive dependence on the interaction strength, in agreement with numerical simulations. We connect this dependence to the ubiquitous logarithmic growth of entanglement entropy characterizing the generic many-body localized phase. Thermofield-based chain mapping approach for open quantum systems de Vega, Ines and Banuls, Mari-Carmen 2015 Abstract: We consider a thermofield approach to analyze the evolution of an open quantum system coupled to an environment at finite temperature. In this approach, the finite temperature environment is exactly mapped onto two virtual environments at zero temperature. These two environments are then unitarily transformed into two different chains of oscillators, leading to a one dimensional structure that can be numerically studied using tensor network techniques. Resonances and Partial Delocalization on the Complete Graph Aizenman, Michael, Shamis, Mira and Warzel, Simone 2014 Abstract: Random operators may acquire extended states formed from a multitude of mutually resonating local quasi-modes. This mechanics is explored here in the context of the random Schrödinger operator on the complete graph. The operators exhibits local quasi modes mixed through a single channel. While most of its spectrum consists of localized eigenfunctions, under appropriate conditions it includes also bands of states which are delocalized in the \ell^1-though not in \ell^2-sense, where the eigenvalues have the statistics of \vSeba spectra. The analysis proceeds through some general observations on the scaling limits of random functions in the Herglotz-Pick class. The results are in agreement with a heuristic condition for the emergence of resonant delocalization, which is stated in terms of the tunneling amplitude among quasi-modes. Decoherence of an entangled state of a strongly-correlated double quantum dot structure through tunneling processes A. Büsser, C., de Vega, I. and Heidrich-Meisner, F. 2014 Abstract: We consider two quantum dots described by the Anderson-impurity model with one electron per dot. The goal of our work is to study the decay of a maximally entangled state between the two electrons localized in the dots. We prepare the system in a perfect singlet and then tunnel-couple one of the dots to leads, which induces the non-equilibrium dynamics. We identify two cases: if the leads are subject to a sufficiently large voltage and thus a finite current, then direct tunneling processes cause decoherence and the entanglement as well as spin correlations decay exponentially fast. At zero voltage or small voltages and beyond the mixed-valence regime, virtual tunneling processes dominate and lead to a slower loss of coherence. We analyze this problem by studying the real-time dynamics of the spin correlations and the concurrence using two techniques, namely the time-dependent density matrix renormalization group method and a master-equation method. The results from these two approaches are in excellent agreement in the direct-tunneling regime for the case in which the dot is weakly tunnel-coupled to the leads. We present a quantitative analysis of the decay rates of the spin correlations and the concurrence as a function of tunneling rate, interaction strength, and voltage. Mean-field phase diagram of the Bose-Fermi Hubbard model Bukov, Marin and Pollet, Lode Phys. Rev. B , Volume 89, page: 094502 2014 Abstract: We analyze the ground-state properties of mixtures consisting of scalar bosons and spin-12 fermions using a mean-field treatment of the local boson-fermion interaction on a simple cubic lattice. In the deep superfluid limit of the boson sector and the BCS regime of the fermion sector, we derive BCS-type equations to determine the phase diagram of the system. We find a competition between a charge density wave and a superconducting phase. In the opposite limit, we study the Mott-insulator-to-superfluid transition of the boson sector in the presence of a staggered density-induced alternating potential provided by the fermions, and determine the mean-field transition line. In the two-superfluids phase of the mixture, we restrict to nearest-neighbor-induced interactions between the fermions and consider the extended Hubbard model. We perform a mean-field analysis of the critical temperature for the formation of boson-assisted s-, extended s−-, d-, and p-wave pairs at fermionic half-filling. We compare our results with a recent dynamical mean-field study [P. Anders et al., Phys. Rev. Lett. 109, 206401 (2012)]. Universal Conductivity in a Two-Dimensional Superfluid-to-Insulator Quantum Critical System Chen, Kun, Liu, Longxiang, Deng, Youjin, Pollet, Lode and Prokof'ev, Nikolay Phys. Rev. Lett. , Volume 112, page: 030402 2014 Abstract: We compute the universal conductivity of the (2+1)-dimensional XY universality class, which is realized for a superfluid-to-Mott insulator quantum phase transition at constant density. Based on large-scale Monte Carlo simulations of the classical (2+1)-dimensional J-current model and the two-dimensional Bose-Hubbard model, we can precisely determine the conductivity on the quantum critical plateau, σ(∞)=0.359(4)σQ with σQ the conductivity quantum. The universal conductivity curve is the standard example with the lowest number of components where the bottoms-up AdS/CFT correspondence from string theory can be tested and made to use [R. C. Myers, S. Sachdev, and A. Singh, Phys. Rev. D 83, 066017 (2011)]. For the first time, the shape of the σ(iωn)−σ(∞) function in the Matsubara representation is accurate enough for a conclusive comparison and establishes the particlelike nature of charge transport. We find that the holographic gauge-gravity duality theory for transport properties can be made compatible with the data if temperature of the horizon of the black brane is different from the temperature of the conformal field theory. The requirements for measuring the universal conductivity in a cold gas experiment are also determined by our calculation. Dipoles in Graphene Have Infinitely Many Bound States Cuenin, Jean-Claude and Siedentop, Heinz 2014 Abstract: We show that in graphene charge distributions with non-vanishing dipole moment have infinitely many bound states. The corresponding eigenvalues accumulate at the edges of the gap faster than any power. An Aharonov-Bohm interferometer for determining Bloch band topology Duca, Lucia, Li, Tracy, Reitter, Martin, Bloch, Immanuel, Schleier-Smith, Monika and Schneider, Ulrich 2014 Abstract: The geometric structure of an energy band in a solid is fundamental for a wide range of many-body phenomena in condensed matter and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. In analogy to an Aharonov-Bohm interferometer that measures the magnetic flux penetrating a given area in real space, we realize an atomic interferometer to measure Berry flux in momentum space. We demonstrate the interferometer for a graphene-type hexagonal lattice, where it has allowed us to directly detect the singular π Berry flux localized at each Dirac point. We show that the interferometer enables one to determine the distribution of Berry curvature with high momentum resolution. Our work forms the basis for a general framework to fully characterize topological band structures and can also facilitate holonomic quantum computing through controlled exploitation of the geometry of Hilbert space. Polynomial cubic differentials and convex polygons in the projective plane Dumas, David and Wolf, Michael 2014 Abstract: We construct and study a natural homeomorphism between the moduli space of polynomial cubic differentials of degree d on the complex plane and the space of projective equivalence classes of oriented convex polygons with d+3 vertices. This map arises from the construction of a complete hyperbolic affine sphere with prescribed Pick differential, and can be seen as an analogue of the Labourie-Loftin parameterization of convex RP^2 structures on a compact surface by the bundle of holomorphic cubic differentials over Teichmuller space. Multiparticle localization for disordered systems on continuous space via the fractional moment method Fauser, Michael and Warzel, Simone 2014 Abstract: We investigate spectral and dynamical localization of a quantum system of n particles on \mathbbR^d which are subject to a random potential and interact through a pair potential which may have infinite range. We establish two conditions which ensure spectral and dynamical localization near the bottom of the spectrum of the n -particle system: i)localization is established in the regime of weak interactions supposing one-particle localization, and ii)localization is also established under a Lifshitz-tail type condition on the sparsity of the spectrum. In case of polynomially decaying interactions, we provide an upper bound on the number of particles up to which these conditions apply.
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