Stroboscopic high-order nonlinearity for quantum optomechanics

High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables. Levitated optomechanics, a field where motion of dielectric particles is driven by precisely controlled tweezer beams, is capable of attaining the required nonlinearity via engineered potential landscapes of mechanical motion. Importantly, to achieve nonlinear quantum effects, the evolution caused by the free motion of mechanics and thermal decoherence have to be suppressed. For this purpose, we devise a method of stroboscopic application of a highly nonlinear potential to a mechanical oscillator that leads to the motional quantum non-Gaussian states exhibiting nonclassical negative Wigner function and squeezing of a nonlinear combination of mechanical quadratures. We test the method numerically by analysing highly instable cubic potential with relevant experimental parameters of the levitated optomechanics, prove its feasibility within reach, and propose an experimental test. The method paves a road for unique experiments instantaneously transforming a ground state of mechanical oscillators to applicable nonclassical states by nonlinear optical force.Comment: 13+8 pages, 2+3 figures. Close to the published versio

Geometry of entanglement witnesses for two qutrits

We characterize a convex subset of entanglement witnesses for two qutrits. Equivalently, we provide a characterization of the set of positive maps in the matrix algebra of 3 x 3 complex matrices. It turns out that boundary of this set displays elegant representation in terms of SO(2) rotations. We conjecture that maps parameterized by rotations are optimal, i.e. they provide the strongest tool for detecting quantum entanglement. As a byproduct we found a new class of decomposable entanglement witnesses parameterized by improper rotations from the orthogonal group O(2).Comment: 9 page

Pulsed quantum continuous-variable optoelectromechanical transducer

We propose a setup allowing to entangle two directly non-interacting radiation modes applying four sequential pulsed quantum resonant interactions with a noisy vibrational mode of a mechanical oscillator which plays the role of the mediator. We analyze Gaussian entanglement of the radiation modes generated by the transducer and confirm that the noisy mechanical mode can mediate generation of entanglement. The entanglement, however, is limited if the interaction gains are not individually optimized. We prove the robustness of the transducer to optical losses and the influence of the mechanical bath and propose the ways to achieve maximal performance through the individual optimization.Comment: 12 pages, 4 figure

Fitting State Space Models with EViews

This paper demonstrates how state space models can be fitted in EViews. We first briefly introduce EViews as an econometric software package. Next we fit a local level model to the Nile data. We then show how a multivariate âÂÂlatent riskâ model can be developed, making use of the EViews programming environment. We conclude by summarizing the possibilities and limitations of the software package when it comes to state space modeling.