Unnested islands of period-doublings in an injected semiconductor laser

We present a theoretical study of unnested period-doubling islands in three-dimensional rate equations modeling a semiconductor laser subject to external optical injection. In this phenomenon successive curves of period doublings are not arranged in nicely nested islands, but intersect each other. This overall structure is globally organized by several codimension-2 bifurcations. As a consequence, the chaotic region existing inside an unnested island of period doublings can be entered not only via a period-doubling cascade but also via the breakup of a torus, and even via the sudden appearance of a chaotic attractor. In order to fully understand these different chaotic transitions we reveal underlying global bifurcations and we show how they are connected to codimension-2 bifurcation points. Unnested islands of period doublings appear to be generic and hence must be expected in a large class of dynamical systems

Pure scaling operators at the integer quantum Hall plateau transition

Stationary wave functions at the transition between plateaus of the integer quantum Hall effect are known to exhibit multi-fractal statistics. Here we explore this critical behavior for the case of scattering states of the Chalker-Coddington model with point contacts. We argue that moments formed from the wave amplitudes of critical scattering states decay as pure powers of the distance between the points of contact and observation. These moments in the continuum limit are proposed to be correlations functions of primary fields of an underlying conformal field theory. We check this proposal numerically by finite-size scaling. We also verify the CFT prediction for a 3-point function involving two primary fields.Comment: Published version, 4 pages, 3 figure

Statistics of conductance and shot-noise power for chaotic cavities

We report on an analytical study of the statistics of conductance, $g$, and shot-noise power, $p$, for a chaotic cavity with arbitrary numbers $N_{1,2}$ of channels in two leads and symmetry parameter $\beta = 1,2,4$. With the theory of Selberg's integral the first four cumulants of $g$ and first two cumulants of $p$ are calculated explicitly. We give analytical expressions for the conductance and shot-noise distributions and determine their exact asymptotics near the edges up to linear order in distances from the edges. For $0<g<1$ a power law for the conductance distribution is exact. All results are also consistent with numerical simulations.Comment: 7 pages, 3 figures. Proc. of the 3rd Workshop on Quantum Chaos and Localisation Phenomena, Warsaw, Poland, May 25-27, 200

Multipulse excitability in injected lasers

We show that a single-mode semiconductor laser subject to optical injection, and described by rate equations, can produce excitable multipulses, where the laser emits a certain number of pulses after being triggered from its steady state by a single perturbation. This phenomenon occurs in experimentally accessible regions in parameter space that are bounded by curves of n-homoclinic bifurcations, connecting a saddle to itself only at the n-threturn to a neighborhood of the saddle. These regions are organised in what we call 'homoclinic teeth' that grow in size and shape with the linewidth enhancement factor

Complex dynamics of an optically injected semiconductor laser : bifurcation theory and experiment

In this paper unprecedented agreement is reported between a theoretical two-dimensional bifurcation diagram and the corresponding experimental stability map of an optically injected semiconductor laser over a large range of relevant injection parameter values. The bifurcation diagram encompasses both local and global bifurcations mapping out regions of regular, chaotic and multistable behavior in considerable detail

Quantum entanglement and teleportation in pulsed cavity-optomechanics

Entangling a mechanical oscillator with an optical mode is an enticing and yet a very challenging goal in cavity optomechanics. Here we consider a pulsed scheme to create Einstein-Podolsky-Rosen-type entanglement between a traveling-wave light pulse and a mechanical oscillator. The entanglement can be verified unambiguously by a pump-probe sequence of pulses. In contrast to schemes that work in a steady-state regime under a continuous-wave drive, this protocol is not subject to stability requirements that normally limit the strength of achievable entanglement. We investigate the protocol's performance under realistic conditions, including mechanical decoherence, in full detail. We discuss the relevance of a high mechanical Qf product for entanglement creation and provide a quantitative statement on which magnitude of the Qf product is necessary for a successful realization of the scheme. We determine the optimal parameter regime for its operation and show it to work in current state-of-the-art systems.Comment: 10 pages, 2 figure

Multipulse excitability in a semiconductor laser with optical injection

A deterministic mechanism for multipulse excitability that appears to be experimentally accessible in a real laser is presented. Codimension-two homoclinic Belyakov bifurcations and an ensuing cascade of n-homoclinic bifurcation tongues are described as responsible for this phenomenon