First iteration within the high-frequency Floquet theory of laser-atom interactions

Solvable Model of a Generic Driven Mixture of Trapped Bose-Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose-Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose-Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose-Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

Fractal scattering in a radiation field

We examine the transfer matrix and the stepping times for chaotic scattering of the excess electron in the chlorine ion Cl(-) from the chlorine atom. We use this information to determine the fraction of incident trajectories that are reflected and transmitted for those electrons caught in the tendrils of the chaotic scattering process.

Dynamics of quasibound state formation in the driven Gaussian potential

The quasibound states of a particle in an inverted-Gaussian potential interacting with an intense laser field are studied using complex coordinate scaling and Floquet theory. The dynamics of the driven system is different depending on whether the driving field frequency is less than or greater than the ionization frequency. As the laser field strength is increased, a new quasibound state emerges as the result of a pitchfork bifurcation in the classical phase space. Changes in the time-averaged "dressed potential" appear related to this bifurcation and provide additional confirmation of the role of the bifurcation on the emergence of a new quasibound state. The Husimi plots of the quasibound state residues reveal strong support on the periodic orbits of the bifurcation at frequencies above the ionization frequency.

Construction of a natural partition of incomplete horseshoes

We present a method for constructing a partition of an incomplete horseshoe in a Poincare map. The partition is based only on the unstable manifolds of the outermost fixed points and eventually their limits. Consequently, this partition becomes natural from the point of view of asymptotic scattering observations. The symbolic dynamics derived from this partition coincides with the one derived from the hierarchical structure of the singularities of the scattering functions.

Classical scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set

We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate Poincaré surface of section. We find the development parameters that describe the hyperbolic component of the chaotic invariant set. In addition, we show that the hierarchical structure of the fractal set of singularities of the scattering functions is the same as the structure of the chaotic invariant set. Finally, we construct a symbolic encoding of the hierarchical structure of the set of singularities of the scattering functions and use concepts from the thermodynamical formalism to obtain one of the measures of chaos of the fractal set of singularities, the topological entropy.

Time independent description of rapidly oscillating potentials

The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the frequency (omega) to order omega(-4). The work is an extension of the classical result for the Kapitza pendulum, which was calculated in the past to order omega(-2). The analysis makes use of an implementation of the method of separation of time scales and of a quantum gauge transformation in the framework of Floquet theory. The effective time independent Hamiltonian enables one to explore the dynamics in the presence of rapidly oscillating fields, in the framework of theories that were developed for systems with time independent Hamiltonians. The results are relevant, in particular, for exploring the dynamics of cold atoms.