Fast light, slow light, and phase singularities: a connection to generalized weak values

We demonstrate that Aharonov-Albert-Vaidman (AAV) weak values have a direct relationship with the response function of a system, and have a much wider range of applicability in both the classical and quantum domains than previously thought. Using this idea, we have built an optical system, based on a birefringent photonic crystal, with an infinite number of weak values. In this system, the propagation speed of a polarized light pulse displays both superluminal and slow light behavior with a sharp transition between the two regimes. We show that this system's response possesses two-dimensional, vortex-antivortex phase singularities. Important consequences for optical signal processing are discussed.Comment: 9 pages, 4 figures, accepted in Physical Review Letters (2003

Liouville Field Theory on an Unoriented Surface

Liouville field theory on an unoriented surface is investigated, in particular, the one point function on a RP^2 is calculated. The constraint of the one point function is obtained by using the crossing symmetry of the two point function. There are many solutions of the constraint and we can choose one of them by considering the modular bootstrap.Comment: 13 pages, no figures, LaTeX, minor changes, equations in section 4 are correcte

High rate, long-distance quantum key distribution over 250km of ultra low loss fibres

We present a fully automated quantum key distribution prototype running at 625 MHz clock rate. Taking advantage of ultra low loss fibres and low-noise superconducting detectors, we can distribute 6,000 secret bits per second over 100 km and 15 bits per second over 250km

Crosscap States for Orientifolds of Euclidean AdS_3

Crosscap states for orientifolds of Euclidean AdS_3 are constructed. We show that our crosscap states describe the same orientifolds which were obtained by the classical analysis. The spectral density of open strings in the system with orientifold can be read from the M"obius strip amplitudes and it is compared to that of the open strings stretched between branes and their mirrors. We also compute the Klein bottle amplitudes.Comment: 17 pages, LaTeX2e, v2: clarification and discussion added, v3: minor changes, to appear in JHE

Standard and Null Weak Values

Weak value (WV) is a quantum mechanical measurement protocol, proposed by Aharonov, Albert, and Vaidman. It consists of a weak measurement, which is weighed in, conditional on the outcome of a later, strong measurement. Here we define another two-step measurement protocol, null weak value (NVW), and point out its advantages as compared to WV. We present two alternative derivations of NWVs and compare them to the corresponding derivations of WVs.Comment: 11 pages, 2 figures. To appear in Quantum Theory: A Two-Time Success Story: Yakir Aharonov Festschrif

Large violation of Bell inequalities with low entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order $\frac{\sqrt{n}}{\log n}$ with $n$ inputs, $n$ outputs and $n$-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the Entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.Comment: Reference [16] added. Some typos correcte

Branch Rings, Thinned Rings, Tree Enveloping Rings

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).Comment: 35 pages; small changes wrt previous versio

PyCOOL - a Cosmological Object-Oriented Lattice code written in Python

There are a number of different phenomena in the early universe that have to be studied numerically with lattice simulations. This paper presents a graphics processing unit (GPU) accelerated Python program called PyCOOL that solves the evolution of scalar fields in a lattice with very precise symplectic integrators. The program has been written with the intention to hit a sweet spot of speed, accuracy and user friendliness. This has been achieved by using the Python language with the PyCUDA interface to make a program that is easy to adapt to different scalar field models. In this paper we derive the symplectic dynamics that govern the evolution of the system and then present the implementation of the program in Python and PyCUDA. The functionality of the program is tested in a chaotic inflation preheating model, a single field oscillon case and in a supersymmetric curvaton model which leads to Q-ball production. We have also compared the performance of a consumer graphics card to a professional Tesla compute card in these simulations. We find that the program is not only accurate but also very fast. To further increase the usefulness of the program we have equipped it with numerous post-processing functions that provide useful information about the cosmological model. These include various spectra and statistics of the fields. The program can be additionally used to calculate the generated curvature perturbation. The program is publicly available under GNU General Public License at https://github.com/jtksai/PyCOOL . Some additional information can be found from http://www.physics.utu.fi/tiedostot/theory/particlecosmology/pycool/ .Comment: 23 pages, 12 figures; some typos correcte

Tree-Level Stability Without Spacetime Fermions: Novel Examples in String Theory

Is perturbative stability intimately tied with the existence of spacetime fermions in string theory in more than two dimensions? Type 0'B string theory in ten-dimensional flat space is a rare example of a non-tachyonic, non-supersymmetric string theory with a purely bosonic closed string spectrum. However, all known type 0' constructions exhibit massless NSNS tadpoles signaling the fact that we are not expanding around a true vacuum of the theory. In this note, we are searching for perturbatively stable examples of type 0' string theory without massless tadpoles in backgrounds with a spatially varying dilaton. We present two examples with this property in non-critical string theories that exhibit four- and six-dimensional Poincare invariance. We discuss the D-branes that can be embedded in this context and the type of gauge theories that can be constructed in this manner. We also comment on the embedding of these non-critical models in critical string theories and their holographic (Little String Theory) interpretation and propose a general conjecture for the role of asymptotic supersymmetry in perturbative string theory.Comment: harvmac, 29 pages; v2 minor changes, version to appear in JHE

Two novel approaches for photometric redshift estimation based on SDSS and 2MASS databases

We investigate two training-set methods: support vector machines (SVMs) and Kernel Regression (KR) for photometric redshift estimation with the data from the Sloan Digital Sky Survey Data Release 5 and Two Micron All Sky Survey databases. We probe the performances of SVMs and KR for different input patterns. Our experiments show that the more parameters considered, the accuracy doesn't always increase, and only when appropriate parameters chosen, the accuracy can improve. Moreover for different approaches, the best input pattern is different. With different parameters as input, the optimal bandwidth is dissimilar for KR. The rms errors of photometric redshifts based on SVM and KR methods are less than 0.03 and 0.02, respectively. Finally the strengths and weaknesses of the two approaches are summarized. Compared to other methods of estimating photometric redshifts, they show their superiorities, especially KR, in terms of accuracy.Comment: accepted for publication in ChJA