Quantum signatures in quadratic optomechanics

We analyze quantum effects occurring in optomechanical systems where the coupling between an optical mode and a mechanical mode is quadratic in displacement (membrane-in-the-middle geometry). We show that it is possible to observe quantum effects in these systems without achieving the single-photon strong coupling regime. We find that zero-point energy causes a mechanical frequency shift, and we propose an experimental way to measure it. Further, we show that it is possible to determine the phonon statistics from the cavity transmission, and propose a way to infer the resonator's temperature based on this feature. For completeness, we revisit the case of an isolated system and show that different types of mechanical quantum states can be created, depending on the initial cavity state. In this situation, mechanical motion undergoes collapse and revivals, and we compute the collapse and revival times, as well as the degree of squeezing.Comment: 7 pages, 6 figures, 2nd versio

A Mechatronic Approach to Control of 6 DOF Parallel Manipulator

This paper presents a practical implementation, using reconfigurable computing applied to robotic problems. Through the proposal a hierarchical architecture, distributing the several control actions in growing levels of complexity and using resources of reconfigurable computing is possible to take into account the easiness of future modifications, updates and improvements in the robotic applications. A practical example is presenting using reconfigurable computing, of Stewart- Gough platform control, where the developed software and hardware are structured in independent blocks, through open architecture implementation, allowing the easy expansion of the system, better adapting the platform to the tasks associated to it. This open architecture implementation allows an easy expansion of the system and a better adaptation of the platform to its related tasks.N/

The type N Karlhede bound is sharp

We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spacetimes are properly $CH_2$, i.e., curvature homogeneous of order 2 but non-homogeneous. This means that tetrad components of $R, \nabla R, \nabla^{(2)}R$ are constant, and that essential coordinates first appear as components of $\nabla^{(3)}R$. Covariant derivatives of orders 4,5,6 yield one additional invariant each, and $\nabla^{(7)}R$ is needed for invariant classification. Thus, our class proves that the bound of 7 on the order of the covariant derivative, first established by Karlhede, is sharp. Our finding corrects an outstanding assertion that invariant classification of four-dimensional Lorentzian manifolds requires at most $\nabla^{(6)}R$.Comment: 7 pages, typos corrected, added citation and acknowledgemen

Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page