Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

General foundation for the nonlinear ponderomotive four-force in laser-plasma interactions

The interaction of electromagnetic radiation with plasmas is studied in relativistic four-vector formalism. A gauge and Lorentz invariant ponderomotive four-force is derived from the time dependent nonlinear three-force of Hora (1985). This four-force, due to its Lorentz invariance, contains new magnetic field terms. A new gauge and Lorentz invariant model of the response of plasma to electromagnetic radiation is then devised. An expression for the dispersion relation is obtained from this model. It is then proved that the magnetic permeability of plasma is unity for a general reference frame. This is an important result since it has been previously assumed in many plasma models.

Watching the brain oscillate: Identifying the neural correlates of illusory jitter

Moving borders defined by small luminance changes (or colour) can appear to jitter at a characteristic frequency when they are placed in close proximity to moving borders defined by large luminance changes (Arnold & Johnston, 2003). Using psychophysical techniques, we have now shown that illusory jitter can be generated when these different motion signals are shown selectively to either eye – implicating a cortical locus for illusory jitter generation. Using magneto-enceohalography (MEG) to record brain activity, we have also found that brain oscillations, of the same frequency as the illusory jitter rate, are enhanced when illusory jitter is experienced. This does not occur when observers are exposed to either isolated motion signals defined by small luminance changes (or colour) or to physical jitter of the same frequency as the illusory jitter. We believe therefore that the enhanced brain activity is related to illusory jitter generation rather than to jitter perception, or to isoluminant motion, per se. These observations support our hypothesis that this illusory jitter is generated in cortex by a dynamic feedback circuit. We believe that this circuit periodically corrects for a spatial conflict generated by proximate motion signals that differ in perceived speed.