Stochastic calculus for convoluted L\'{e}vy processes

We develop a stochastic calculus for processes which are built by convoluting a pure jump, zero expectation L\'{e}vy process with a Volterra-type kernel. This class of processes contains, for example, fractional L\'{e}vy processes as studied by Marquardt [Bernoulli 12 (2006) 1090--1126.] The integral which we introduce is a Skorokhod integral. Nonetheless, we avoid the technicalities from Malliavin calculus and white noise analysis and give an elementary definition based on expectations under change of measure. As a main result, we derive an It\^{o} formula which separates the different contributions from the memory due to the convolution and from the jumps.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ115 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Pseudomagnetic fields for sound at the nanoscale

There is a growing effort in creating chiral transport of sound waves. However, most approaches so far are confined to the macroscopic scale. Here, we propose a new approach suitable to the nanoscale which is based on pseudomagnetic fields. These fields are the analogon for sound of the pseudomagnetic field for electrons in strained graphene. In our proposal, they are created by simple geometrical modifications of an existing and experimentally proven phononic crystal design, the snowflake crystal. This platform is robust, scalable, and well-suited for a variety of excitation and readout mechanisms, among them optomechanical approaches

Optical investigations on PTCDA on KCl(100) : Superradiant aggregates and single molecules

In the present work, condensed and diluted phases of 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA) were investigated on thin KCl(100) films on the Ag(100) surface. The samples were structurally characterized by spot profile analysis low energy electron diffraction (SPA-LEED), and bright field microscopy. The optical properties of the samples were investigated by fluorescence spectroscopy (FL), fluorescence excitation spectroscopy (FLE), and fluorescence microscopy. The work tackled three advanced questions of the so far already quite well understood sample system. I The optical and structural properties of the condensed PTCDA/KCl(100) brickwall phase were reinvestigated for improved preparation conditions and an extended temperature range. Here a focus lied on the enhancement of the pure electronic transition with respect to the vibronic modes, called superradiance. The temperature dependence of the superradiance showed an atypical initial rise in the low temperature regime and could be explained by a theory based on finite size effects. It could be shown that the atypical low temperature behavior is the result of node planes in the wavefunctions of the excitonic ground states of brickwall-type aggregates. The node planes are induced by weak repulsive next-nearest-neighbor interactions and become dominant in the case of highly asymmetric aggregates. The experimental temperature dependence could be simulated by weighting the calculated temperature dependencies of individual aggregates with a domain size distribution extracted from a detailed SPA-LEED analysis. II The homogeneous line profiles of single PTCDA molecules located at KCl-step edge sites were investigated by high resolution single molecule FLE spectroscopy. Here first a splitting of the inhomogeneous broadening into two main species could be observed. On top of the inhomogeneous broadening a statistical fine structure consisting of individual homogeneously broadened single molecule profiles was observed. Far off the center of the inhomogeneous profile, also spectrally isolated single molecule profiles were measured. The FLE measurements of these single molecules adsorbed on a surface revealed a molecular behavior qualitatively equivalent to that observed in earlier single molecule studies on molecules in solid hosts. This includes aspects as: the width and the form of the absorption profiles, the saturation behavior with the intensity of the excitation light, an observed broadening with temperature, and a tendency to undergo laser induced and independent spectral jumps. III An UHV compatible light microscope for the brightfield and fluorescence application was developed and used to study the macroscopic surface morphology and the fluorescence signal from molecules on the sample surface. The microscope was developed for the investigation of samples under ultra high vacuum conditions and images the surface through a glass window. Bright field images of the sample revealed a characteristic mesoscopic corrugation and a variety of local defects. In the fluorescence images, a mostly homogeneous coverage of the sample could be proven. However, also exceptions from this homogeneity were observed and could be correlated with the sample morphology. These included shading effects of mesoscopic surface protrusions related to an inclined angle of the molecular beam, occasional intensity variations presumably due to a local inhomogeneity of the KCl film thickness, and very local and bright fluorescence signals at some special surface defects

Pattern phase diagram for 2D arrays of coupled limit-cycle oscillators

Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. They are also of direct relevance in the context of currently emerging experiments on nano- and optomechanical oscillator arrays. We find that the full dynamical equations for the phase dynamics of such an array go beyond previously studied Kuramoto-type equations. We analyze the evolution of the phase field in a two-dimensional array and obtain a "phase diagram" for the resulting stationary and non-stationary patterns. The possible observation in optomechanical arrays is discussed briefly

Quantum Cloning of Binary Coherent States - Optimal Transformations and Practical Limits

The notions of qubits and coherent states correspond to different physical systems and are described by specific formalisms. Qubits are associated with a two-dimensional Hilbert space and can be illustrated on the Bloch sphere. In contrast, the underlying Hilbert space of coherent states is infinite-dimensional and the states are typically represented in phase space. For the particular case of binary coherent state alphabets these otherwise distinct formalisms can equally be applied. We capitalize this formal connection to analyse the properties of optimally cloned binary coherent states. Several practical and near-optimal cloning schemes are discussed and the associated fidelities are compared to the performance of the optimal cloner.Comment: 12 pages, 12 figure

Topological phase transitions and chiral inelastic transport induced by the squeezing of light

We show how the squeezing of light can lead to the formation of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a Kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits.Comment: 11 pages, 4 figure