Driven-Dissipative Dynamics of Atomic Ensembles in a Resonant Cavity II: Quasiperiodic Route to Chaos and Chaotic Synchronization

We analyze the origin and properties of the chaotic dynamics of two atomic ensembles in a driven-dissipative experimental setup, where they are collectively damped by a bad cavity mode and incoherently pumped by a Raman laser. Starting from the mean-field equations, we explain the emergence of chaos by way of quasiperiodicity -- presence of two or more incommensurate frequencies. This is known as the Ruelle-Takens-Newhouse route to chaos. The equations of motion have a $\mathbb{Z}_{2}$-symmetry with respect to the interchange of the two ensembles. However, some of the attractors of these equations spontaneously break this symmetry. To understand the emergence and subsequent properties of various attractors, we concurrently study the mean-field trajectories, Poincar\'{e} sections, maximum and conditional Lyapunov exponents, and power spectra. Using Floquet analysis, we show that quasiperiodicity is born out of non $\mathbb{Z}_{2}$-symmetric oscillations via a supercritical Neimark-Sacker bifurcation. Changing the detuning between the level spacings in the two ensembles and the repump rate results in the synchronization of the two chaotic ensembles. In this regime, the chaotic intensity fluctuations of the light radiated by the two ensembles are identical. Identifying the synchronization manifold, we understand the origin of synchronized chaos as a tangent bifurcation intermittency of the $\mathbb{Z}_{2}$-symmetric oscillations. At its birth, synchronized chaos is unstable. The interaction of this attractor with other attractors causes on-off intermittency until the synchronization manifold becomes sufficiently attractive. We also show coexistence of different phases in small pockets near the boundaries.Comment: 52 pages, 36 figures, published versio

Dynamical chaos in the integrable Toda chain induced by time discretization

We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various symplectic integrators parametrized by the time step $\tau$ and measure the Lyapunov time $T_{\Lambda}$ (inverse of the largest Lyapunov exponent $\Lambda$). A key observation is that $T_{\Lambda}$ is finite whenever $\tau$ is finite but diverges when $\tau \rightarrow 0$. We compare the Toda chain results with the nonitegrable Fermi-Pasta-Ulam-Tsingou chain dynamics. In addition, we observe a breakdown of the simulations at times $T_B \gg T_{\Lambda}$ due to certain positions and momenta becoming extremely large (``Not a Number''). This phenomenon originates from the periodic driving introduced by symplectic integrators and we also identify the concrete mechanism of the breakdown in the case of the Toda chain.Comment: 13 pages, 7 figure

Polyvinylpyrrolidone modified barium zirconate titanate/polyvinylidene fluoride nanocomposites as self-powered sensor

Highly flexible biocompatible nanocomposites comprising of Polyvinylpyrrolidone (PVP) modified Barium Calcium Zirconate Titanate (BCT-BZT) /Polyvinylidene fluoride (PVDF) were fabricated. The crystalline BCT-BZT powders were synthesized by a simple sol-gel method. Rietveld refinement analysis confirmed the coexistence of orthorhombic and tetragonal phase in the synthesized powders. The structural, dielectric and ferro-electric properties of the composites were analysed. Addition of PVP modified BCT-BZT powders was observed to enhance the polar phase in PVDF matrix. The piezoelectric output response as a function of different weight percentage of ceramic powders in the PVDF matrix was investigated. The optimal device with 60wt% PVP modified BCT-BZT powders exhibited maximum peak to peak voltage of 23 V when tested for harnessing waste biomechamcal energy (human hand palm force). The nanogenerator was easily scaled up to 4 x 4 cm and the stored power was utilized for powering fifty five LEDs. The fabricated device is flexible, light- weight and eco-friendly Therefore, it can be explored as a potential candidate for application as self powered sensor