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Register a new userSwitching off chaos in two-dimensional optical cavities
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Chaos is generally considered a nuisance, inasmuch as it prevents long-term predictions in physical systems. Here, we present an easily accessible approach to undo deterministic chaos in arbitrary two-dimensional optical chaotic billiards, by introducing spatially varying refractive index therein. The landscape of refractive index is obtained by a conformal transformation from an integrable billiard. Our study shows that this approach is robust to small fluctuations. We show further that trajectory rectification can be realized by relating chaotic billiards with non-Euclidean billiards. Finally, we illustrate the universality of this approach by extending our investigations to arbitrarily deformed optical billiards. This work not only contributes in controlling chaos, but provides a novel pathway to the design of billiards and microcavities with desired properties and functionalities.
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Periodic forcing of nonlinear oscillators generates a rich and complex variety of behaviors, ranging from regular to chaotic behavior. In this work we seek to control, i.e., either suppress or generate, the chaotic behavior of a classical reference example in books or introductory articles, the Duffing oscillator. For this purpose, we propose an elegant strategy consisting of simply adjusting the shape of the time-dependent forcing. The efficiency of the proposed strategy is shown analytically, numerically and experimentally. In addition due to its simplicity and low cost such a work could easily be turned into an excellent teaching tool.
The texture of phase space and bifurcation diagrams of two-dimensional discrete maps describing a lattice of interacting oscillators, confined in on-site potentials with deformable double-well shapes, are examined. The two double-well potentials considered belong to a family proposed by Dikande and Kofane (A. M. Dikande and T. C. Kofane, Solid State Commun. vol. 89, p. 559, 1994), whose shapes can be tuned distinctively: one has a variable barrier height and the other has variable minima positions. However the two parametrized double-well potentials reduce to the $phi^4$ substrate, familiar in the studies of structural phase transitions in centro-symmetric crystals or bistable processes in biophysics. It is shown that although the parametric maps are area preserving their routes to chaos display different characteristic features: the first map exhibits a cascade of period-doubling bifurcations with respect to the potential amplitude, but period-halving bifurcations with respect to the shape deformability parameter. On the other hand the first bifurcation of the second map always coincides with the first pitchfork bifurcation of the $phi^4$ map. However, an increase of the deformability parameter shrinks the region between successive period-doubling bifurcations. The two opposite bifurcation cascades characterizing the first map, and the shrinkage of regions between successive bifurcation cascades which is characteristic of the second map, suggest a non-universal character of the Feigenbaum-number sequences associate with the two discrete parametric double-well maps.
We study and characterize a direct route to high-dimensional chaos (i.e. not implying an intermediate low-dimensional attractor) of a system composed out of three coupled Lorenz oscillators. A geometric analysis of this medium-dimensional dynamical system is carried out through a variety of numerical quantitative and qualitative techniques, that ultimately lead to the reconstruction of the route. The main finding is that the transition is organized by a heteroclinic explosion. The observed scenario resembles the classical route to chaos via homoclinic explosion of the Lorenz model.
The development of solid-state photonic quantum technologies is of great interest for fundamental studies of light-matter interactions and quantum information science. Diamond has turned out to be an attractive material for integrated quantum information processing due to the extraordinary properties of its colour centres enabling e.g. bright single photon emission and spin quantum bits. To control emitted photons and to interconnect distant quantum bits, micro-cavities directly fabricated in the diamond material are desired. However, the production of photonic devices in high-quality diamond has been a challenge so far. Here we present a method to fabricate one- and two-dimensional photonic crystal micro-cavities in single-crystal diamond, yielding quality factors up to 700. Using a post-processing etching technique, we tune the cavity modes into resonance with the zero phonon line of an ensemble of silicon-vacancy centres and measure an intensity enhancement by a factor of 2.8. The controlled coupling to small mode volume photonic crystal cavities paves the way to larger scale photonic quantum devices based on single-crystal diamond.
We uncover a route from low-dimensional to high-dimensional chaos in nonsmooth dynamical systems as a bifurcation parameter is continuously varied. The striking feature is the existence of a finite parameter interval of periodic attractors in between the regimes of low- and high-dimensional chaos. That is, the emergence of high-dimensional chaos is preceded by the systems settling into a totally nonchaotic regime. This is characteristically distinct from the situation in smooth dynamical systems where high-dimensional chaos emerges directly and smoothly from low-dimensional chaos. We carry out an analysis to elucidate the underlying mechanism for the abrupt emergence and disappearance of the periodic attractors and provide strong numerical support for the typicality of the transition route in the pertinent two-dimensional parameter space. The finding has implications to applications where high-dimensional and robust chaos is desired.
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