Positivity of linear maps under tensor powers
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 copositive maps are trivial examples of this kind. We show that for every n∈\mathbbN there exist nontrivial maps with this property and that for twodimensional Hilbert spaces there is no nontrivial map for which this holds for all n. For higher dimensions we reduce the existence question of such nontrivial "tensorstable positive maps" to a oneparameter family of maps and show that an affirmative answer would imply the existence of NPPT bound entanglement. As an application we show that any tensorstable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the wellknown cbnorm bound. We furthermore show that the latter is an upper bound even for the LOCCassisted quantum capacity, and that moreover it is a strong converse rate for this task. 
Linear and Nonlinear Response of Lithographically Defined Plasmonic Nanoantennas
Proceedings of SPIE 9371, 93711D (2015)
2015
Abstract: We present numerical studies, nanofabrication 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 feedgap 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 feedgaps 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 feedgap. Under excitation with a 100fs pulsed laser source, we observed nonlinear light emission arising from twophoton 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. DOI: 10.1117/12.2079104

Observation of manybody localization of interacting fermions in a quasirandom optical lattice
2015
Abstract: We experimentally observe manybody localization of interacting fermions in a onedimensional quasirandom optical lattice. We identify the manybody localization transition through the relaxation dynamics of an initiallyprepared 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 manybody localized phase. 
Thermofieldbased chain mapping approach for open quantum systems
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
2014
Abstract: Random operators may acquire extended states formed from a multitude of mutually resonating local quasimodes. 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^1though not in \ell^2sense, 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 HerglotzPick 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 quasimodes. 
Decoherence of an entangled state of a stronglycorrelated double quantum dot structure through tunneling processes
2014
Abstract: We consider two quantum dots described by the Andersonimpurity 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 tunnelcouple one of the dots to leads, which induces the nonequilibrium 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 mixedvalence regime, virtual tunneling processes dominate and lead to a slower loss of coherence. We analyze this problem by studying the realtime dynamics of the spin correlations and the concurrence using two techniques, namely the timedependent density matrix renormalization group method and a masterequation method. The results from these two approaches are in excellent agreement in the directtunneling regime for the case in which the dot is weakly tunnelcoupled 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. 
Meanfield phase diagram of the BoseFermi Hubbard model
Phys. Rev. B
, Volume 89, page: 094502
2014
Abstract: We analyze the groundstate properties of mixtures consisting of scalar bosons and spin12 fermions using a meanfield treatment of the local bosonfermion 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 BCStype 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 Mottinsulatortosuperfluid transition of the boson sector in the presence of a staggered densityinduced alternating potential provided by the fermions, and determine the meanfield transition line. In the twosuperfluids phase of the mixture, we restrict to nearestneighborinduced interactions between the fermions and consider the extended Hubbard model. We perform a meanfield analysis of the critical temperature for the formation of bosonassisted s, extended s−, d, and pwave pairs at fermionic halffilling. We compare our results with a recent dynamical meanfield study [P. Anders et al., Phys. Rev. Lett. 109, 206401 (2012)]. 
Universal Conductivity in a TwoDimensional SuperfluidtoInsulator Quantum Critical System
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 superfluidtoMott insulator quantum phase transition at constant density. Based on largescale Monte Carlo simulations of the classical (2+1)dimensional Jcurrent model and the twodimensional BoseHubbard 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 bottomsup 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 gaugegravity 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
2014
Abstract: We show that in graphene charge distributions with nonvanishing dipole moment have infinitely many bound states. The corresponding eigenvalues accumulate at the edges of the gap faster than any power. 
An AharonovBohm interferometer for determining Bloch band topology
2014
Abstract: The geometric structure of an energy band in a solid is fundamental for a wide range of manybody phenomena in condensed matter and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. In analogy to an AharonovBohm 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 graphenetype 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
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 LabourieLoftin 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
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 oneparticle localization, and ii)localization is also established under a Lifshitztail 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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