Building a 3.5 m prototype interferometer for the Q & A vacuum birefringence experiment and high precision ellipsometry

We have built and tested a 3.5 m high-finesse Fabry-Perot prototype inteferometer with a precision ellipsometer for the QED test and axion search (Q & A) experiment. We use X-pendulum-double-pendulum suspension designs and automatic control schemes developed by the gravitational-wave detection community. Verdet constant and Cotton-Mouton constant of the air are measured as a test. Double modulation with polarization modulation 100 Hz and magnetic-field modulation 0.05 Hz gives 10^{-7} rad phase noise for a 44-minute integration.Comment: This draft has been presented in the 5th Edoardo Amaldi Conference on Gravitational Wave

A Mesoscopic Resonating Valence Bond system on a triple dot

We introduce a mesoscopic pendulum from a triple dot. The pendulum is fastened through a singly-occupied dot (spin qubit). Two other strongly capacitively islands form a double-dot charge qubit with one electron in excess oscillating between the two low-energy charge states (1,0) and (0,1); this embodies the weight of the pendulum. The triple dot is placed between two superconducting leads as shown in Fig. 1. Under well-defined conditions, the main proximity effect stems from the injection of resonating singlet (valence) bonds on the triple dot. This gives rise to a Josephson current that is charge- and spin-dependent. Consequences in a SQUID-geometry are carefully investigated.Comment: final version to appear in PR

A set oriented approach to global optimal control

We describe an algorithm for computing the value function for 'all source, single destination' discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem on a finite graph. The method is illustrated by two numerical examples, namely a single pendulum on a cart and a parametrically driven inverted double pendulum

Quantum phase space picture of Bose-Einstein Condensates in a double well: Proposals for creating macroscopic quantum superposition states and a study of quantum chaos

We present a quantum phase space model of Bose-Einstein condensate (BEC) in a double well potential. In a two-mode Fock-state analysis we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase space information is extracted from the stationary quantum states using the Husimi distribution function. It is shown that the quantum states are localized on the known classical phase space orbits of a nonrigid physical pendulum, and thus the novel phase space characteristics of a nonrigid physical pendulum such as the $\pi$ motions are seen to be a property of the exact quantum states. Low lying states are harmonic oscillator like libration states while the higher lying states are Schr\"odinger cat-like superpositions of two pendulum rotor states. To study the dynamics in phase space, a comparison is made between a displaced quantum wavepacket and the trajectories of a swarm of points in classical phase space. For a driven double well, it is shown that the classical chaotic dynamics is manifest in the dynamics of the quantum states pictured using the Husimi distribution. Phase space analogy also suggests that a $\pi$ phase displaced wavepacket put on the unstable fixed point on a separatrix will bifurcate to create a superposition of two pendulum rotor states - a Schr\"odinger cat state (number entangled state) for BEC. It is shown that the choice of initial barrier height and ramping, following a $\pi$ phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.Comment: revised version, 13 pages, 13 figure

Pendubot combining of energy and intuitive approach to swing up, stabilization in erected pose

International audienceThe objective of this paper is to define a strategy for the swing up of a doublelink pendulum and its stabilization in the unstable equilibrium state with both erected links. The first joint of this double-link pendulum, which is the suspension joint, is actuated and the second joint is passive. This double-link pendulum, usually called pendubot, is an underactuated system. The double-link pendulum is straightened during the energy boosting process. The swing up control switches to the balancing mode at the instant when the system comes to the basin of attraction. The limits on the torque amplitude are taken into account. The gains of the saturated balancing control are chosen to ensure the basin of attraction as large as possible. Simulation results demonstrate that our strategy is efficient

Fuzzy Optimal Control for Double Inverted Pendulum

In this paper a fuzzy optimal control for stabilizing an upright position a double inverted pendulum (DIP) is developed and compared. Modeling is based on Euler-Lagrange equations. This results in a complicated nonlinear fast reaction, unstable multivariable system. Firstly, the mathematical models of double pendulum system are presented. The weight variable fuzzy input is gained by combining the fuzzy control theory with the optimal control theory. Simulation results show that the controller, which the upper pendulum is considered as main control variable, has high accuracy, quick convergence speed and higher precision

Synchronization of a double pendulum with moving pivots: a study of the spectrum

The model we consider consists in a double pendulum set, where the pivot points are free to shift along a horizontal line. Moreover, the two pendula are coupled by means of a spring whose extremities connect two points of each pendulum, at a fixed distance from the corresponding pivot. The mathematical model is first written encompassing a large class of setting for the device (different sizes, different physical properties, ...). In order to carry on the problem of synchronization via analytical me\-thods, we focus on the circumstance of identical pendula: in that case, some classical theorems concerning the zeroes of polynomial equations are used in order to locate the eigenvalues governing the process, so that the possibility of synchronization of the device can be better understood