Numerical studies of light-matter interaction driven by plasmonic fields: the velocity gauge

Theoretical approaches to strong field phenomena driven by plasmonic fields are based on the length gauge formulation of the laser-matter coupling. From the theoretical viewpoint it is known there exists no preferable gauge and consequently the predictions and outcomes should be independent of this choice. The use of the length gauge is mainly due to the fact that the quantity obtained from finite elements simulations of plasmonic fields is the plasmonic enhanced laser electric field rather than the laser vector potential. In this paper we develop, from first principles, the velocity gauge formulation of the problem and we apply it to the high-order harmonic generation (HHG) in atoms. A comparison to the results obtained with the length gauge is made. It is analytically and numerically demonstrated that both gauges give equivalent descriptions of the emitted HHG spectra resulting from the interaction of a spatially inhomogeneous field and the single active electron (SAE) model of the helium atom. We discuss, however, advantages and disadvantages of using different gauges in terms of numerical efficiency.Comment: 19 pages, 5 figures, submitted to Journal of Computational Physic

Citizenship and Family: Revisiting Dred Scott

This Essay explores the implications of the Dred Scott case for modern questions about family unity as it is affected by U.S. immigration law and policy. Part I elaborates on Dred Scott’s story, illustrating the central role that family unity played in the case. Part II focuses on the arc of history as it extends from Dred Scott to the present, demonstrating that the historical narrative of the Dred Scott case has often been used as a rallying cry for thicker, more robust conceptions of citizenship and for “equal citizenship.” Part III argues that, when it comes to the right to family integrity, a contemporary re-reading of the story of the Dred Scott family and a reexamination of the legacy of the Dred Scott decision might actually favor a decoupling of the right to family integrity and the rights associated with formal citizenship. In lieu of a more robust definition of citizenship that encompasses the right to family integrity, perhaps the Dred Scott case and its aftermath counsel us to move toward a more human-rights centered definition of the right to family integrity, applicable to all persons subject to the jurisdiction of U.S. laws. Part IV concludes that a broader understanding of the right to family would require revisions to certain components of U.S. immigration laws that pose clear, and sometimes unnecessary, barriers to family integrity

Homoclinic Signatures of Dynamical Localization

It is demonstrated that the oscillations in the width of the momentum distribution of atoms moving in a phase-modulated standing light field, as a function of the modulation amplitude, are correlated with the variation of the chaotic layer width in energy of an underlying effective pendulum. The maximum effect of dynamical localization and the nearly perfect delocalization are associated with the maxima and minima, respectively, of the chaotic layer width. It is also demonstrated that kinetic energy is conserved as an almost adiabatic invariant at the minima of the chaotic layer width, and that the system is accurately described by delta-kicked rotors at the zeros of the Bessel functions J_0 and J_1. Numerical calculations of kinetic energy and Lyapunov exponents confirm all the theoretical predictions.Comment: 7 pages, 4 figures, enlarged versio