Trade relationships between the Gulf Cooperation Council and the European Union

This paper examines the trade relationship between the Gulf Cooperation Council (GCC) and the European Union (EU). A simultaneous equation regression model is developed and estimated to assist with the analysis. The regression results, using both the two stage least squares (2SLS) and ordinary least squares (OLS) estimation methods, reveal the existence of feedback effects between the two economic integrations. The results also show that during times of slack in oil prices, the GCC income from its investments overseas helped to finance its imports from the EU.

Transforming chaos to periodic oscillations

We demonstrate that the dynamics of an autonomous chaotic class C laser can be controlled to a periodic state via external modulation of the pump. In the absence of modulation, above the chaos threshold, the laser exhibits Lorenz-like chaotic pulsations. The average amplitude and frequency of these pulsations depend on the pump power. We find that there exist parameter windows where modulation of the pump power extinguishes the chaos in favor of simpler periodic behavior. Moreover we find a number of locking ratios between the pump and laser output follow the Farey sequence.

The effects of time delays in adaptive phase measurements

It is not possible to make measurements of the phase of an optical mode using linear optics without introducing an extra phase uncertainty. This extra phase variance is quite large for heterodyne measurements, however it is possible to reduce it to the theoretical limit of log (n) over bar (4 (n) over bar (2)) using adaptive measurements. These measurements are quite sensitive to experimental inaccuracies, especially time delays and inefficient detectors. Here it is shown that the minimum introduced phase variance when there is a time delay of tau is tau/(8 (n) over bar). This result is verified numerically, showing that the phase variance introduced approaches this limit for most of the adaptive schemes using the best final phase estimate. The main exception is the adaptive mark II scheme with simplified feedback, which is extremely sensitive to time delays. The extra phase variance due to time delays is considered for the mark I case with simplified feedback, verifying the tau /2 result obtained by Wiseman and Killip both by a more rigorous analytic technique and numerically.

Phase sensitive pumping and coherence of superposition states

The continuous parametric pumping of a superconducting lossy QED cavity supporting a field prepared initially as a superposition of coherent states is discussed. In contrast to classical pumping, we verify that the phase sensitivity of the parametric pumping makes the asymptotic behaviour of the cavity field state strongly dependent on the phase theta of the coherent state \ alpha > = \ alpha \e(i theta)>. Here we consider theta = pi /4, -pi /4 and we analyse the evolution of the purity of the superposition states with the help of the linear entropy and fidelity functions. We also analyse the decoherence process quantitatively through the Wigner function, for both states, verifying that the decay is slightly modified when compared to the free decoherence case: for theta = -pi /4 the process is accelerated while for theta = pi /4 it is delayed.

Teleportation with the entangled states of a beam splitter

We present a teleportation protocol based upon the entanglement produced from Fock states incident onto a beam splitter of arbitrary transmissivity. The teleportation fidelity is analyzed, its trends being explained from consideration of a beam splitter's input-output characteristics.