Observation of light dragging in rubidium vapor cell

We report on the experimental demonstration of light dragging effect due to atomic motion in a rubidium vapor cell. We found that the minimum group velocity is achieved for light red-shifted from the center of the atomic resonance, and that the value of this shift increases with decreasing group velocity, in agreement with the theoretical predictions by Kocharovskaya, Rostovtsev, and Scully [Phys. Rev. Lett. {\bf 86}, 628 (2001)].Comment: 4 pages 4 figures, submitted to PR

Quantized Rotation of Atoms From Photons with Orbital Angular Momentum

We demonstrate the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of hbar, using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate of sodium atoms. We show that the process is coherent by creating superpositions of different vortex states, where the relative phase between the states is determined by the relative phases of the optical fields. Furthermore, we create vortices of charge 2 by transferring to each atom the orbital angular momentum of two photons.Comment: New version, 4 pages and 3 figures, accepted for publication in Physical Review Letter

Proper time and Minkowski structure on causal graphs

For causal graphs we propose a definition of proper time which for small scales is based on the concept of volume, while for large scales the usual definition of length is applied. The scale where the change from "volume" to "length" occurs is related to the size of a dynamical clock and defines a natural cut-off for this type of clock. By changing the cut-off volume we may probe the geometry of the causal graph on different scales and therey define a continuum limit. This provides an alternative to the standard coarse graining procedures. For regular causal lattice (like e.g. the 2-dim. light-cone lattice) this concept can be proven to lead to a Minkowski structure. An illustrative example of this approach is provided by the breather solutions of the Sine-Gordon model on a 2-dimensional light-cone lattice.Comment: 15 pages, 4 figure

Exact solution of the Zeeman effect in single-electron systems

Contrary to popular belief, the Zeeman effect can be treated exactly in single-electron systems, for arbitrary magnetic field strengths, as long as the term quadratic in the magnetic field can be ignored. These formulas were actually derived already around 1927 by Darwin, using the classical picture of angular momentum, and presented in their proper quantum-mechanical form in 1933 by Bethe, although without any proof. The expressions have since been more or less lost from the literature; instead, the conventional treatment nowadays is to present only the approximations for weak and strong fields, respectively. However, in fusion research and other plasma physics applications, the magnetic fields applied to control the shape and position of the plasma span the entire region from weak to strong fields, and there is a need for a unified treatment. In this paper we present the detailed quantum-mechanical derivation of the exact eigenenergies and eigenstates of hydrogen-like atoms and ions in a static magnetic field. Notably, these formulas are not much more complicated than the better-known approximations. Moreover, the derivation allows the value of the electron spin gyromagnetic ratio $g_s$ to be different from 2. For completeness, we then review the details of dipole transitions between two hydrogenic levels, and calculate the corresponding Zeeman spectrum. The various approximations made in the derivation are also discussed in details.Comment: 18 pages, 4 figures. Submitted to Physica Script

Some properties of the k-dimensional Lyness' map

This paper is devoted to study some properties of the k-dimensional Lyness' map. Our main result presentes a rational vector field that gives a Lie symmetry for F. This vector field is used, for k less or equal to 5 to give information about the nature of the invariant sets under F. When k is odd, we also present a new (as far as we know) first integral for F^2 which allows to deduce in a very simple way several properties of the dynamical system generated by F. In particular for this case we prove that, except on a given codimension one algebraic set, none of the positive initial conditions can be a periodic point of odd period.Comment: 22 pages; 3 figure

Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything

Zero Determinant (ZD) strategies are a new class of probabilistic and conditional strategies that are able to unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner's Dilemma irrespective of the opponent's strategy, or else to set the ratio between a ZD player's and their opponent's expected payoff. Here we show that while ZD strategies are weakly dominant, they are not evolutionarily stable and will instead evolve into less coercive strategies. We show that ZD strategies with an informational advantage over other players that allows them to recognize other ZD strategies can be evolutionarily stable (and able to exploit other players). However, such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition.Comment: 14 pages, 4 figures. Change in title (again!) to comply with Nature Communications requirements. To appear in Nature Communication

Causal categories: relativistically interacting processes

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a `causal category'. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.Comment: 43 pages, lots of figure

Optics of Nonuniformly Moving Media

A moving dielectric appears to light as an effective gravitational field. At low flow velocities the dielectric acts on light in the same way as a magnetic field acts on a charged matter wave. We develop in detail the geometrical optics of moving dispersionless media. We derive a Hamiltonian and a Lagrangian to describe ray propagation. We elucidate how the gravitational and the magnetic model of light propagation are related to each other. Finally, we study light propagation around a vortex flow. The vortex shows an optical Aharonov--Bohm effect at large distances from the core, and, at shorter ranges, the vortex may resemble an optical black hole.Comment: Physical Review A (submitted

Analysis of a three-component model phase diagram by Catastrophe Theory

We analyze the thermodynamical potential of a lattice gas model with three components and five parameters using the methods of Catastrophe Theory. We find the highest singularity, which has codimension five, and establish its transversality. Hence the corresponding seven-degree Landau potential, the canonical form Wigwam or $A_6$, constitutes the adequate starting point to study the overall phase diagram of this model.Comment: 16 pages, Latex file, submitted to Phys. Rev.

The role of inhibitory feedback for information processing in thalamocortical circuits

The information transfer in the thalamus is blocked dynamically during sleep, in conjunction with the occurence of spindle waves. As the theoretical understanding of the mechanism remains incomplete, we analyze two modeling approaches for a recent experiment by Le Masson {\sl et al}. on the thalamocortical loop. In a first step, we use a conductance-based neuron model to reproduce the experiment computationally. In a second step, we model the same system by using an extended Hindmarsh-Rose model, and compare the results with the conductance-based model. In the framework of both models, we investigate the influence of inhibitory feedback on the information transfer in a typical thalamocortical oscillator. We find that our extended Hindmarsh-Rose neuron model, which is computationally less costly and thus siutable for large-scale simulations, reproduces the experiment better than the conductance-based model. Further, in agreement with the experiment of Le Masson {\sl et al}., inhibitory feedback leads to stable self-sustained oscillations which mask the incoming input, and thereby reduce the information transfer significantly.Comment: 16 pages, 15eps figures included. To appear in Physical Review