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 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 exploration of the dynamics of cold atoms.Comment: 4 pages, 1 figure. Revised versio

Analogue of the quantum hanle effect and polarization conversion in non-hermitian plasmonic metamaterials

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Nano Letters, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://pubs.acs.org/page/policy/articlesonrequest/index.htmlThe Hanle effect, one of the first manifestations of quantum theory introducing the concept of coherent superposition between pure states, plays a key role in numerous aspects of science varying from applicative spectroscopy to fundamental astrophysical investigations. Optical analogues of quantum effects help to achieve deeper understanding of quantum phenomena and, in turn, to develop cross-disciplinary approaches to realizations of new applications in photonics. Here we show that metallic nanostructures can be designed to exhibit a plasmonic analogue of the quantum Hanle effect and the associated polarization rotation. In the original Hanle effect, time-reversal symmetry is broken by a static magnetic field. We achieve this by introducing dissipative level crossing of localized surface plasmons due to nonuniform losses, designed using a non-Hermitian formulation of quantum mechanics. Such artificial plasmonic "atoms" have been shown to exhibit strong circular birefringence and circular dichroism which depends on the value of loss or gain in the metal-dielectric nanostructure. © 2012 American Chemical Society.This work has been supported in part by EPSRC (UK). P.G. acknowledges Royal Society for a Newton International Fellowship. F.J.R.-F. acknowledges support from grant FPI of GV and the Spanish MICINN under contracts CONSOLIDER EMET CSD2008-00066 and TEC2011-28664-C02-02.Ginzburg, P.; Rodríguez Fortuño, FJ.; Martínez Abietar, AJ.; Zayats, AV. (2012). Analogue of the quantum hanle effect and polarization conversion in non-hermitian plasmonic metamaterials. Nano Letters. 12(12):6309-6314. https://doi.org/10.1021/nl3034174S63096314121

Exceptional points in a non-Hermitian extension of the Jaynes-Cummings Hamiltonian

We consider a generalization of the non-Hermitian PT symmetric Jaynes-Cummings Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay. In particular, we investigate the interaction of a two-level fermionic system (such as a two-level atom) with a single bosonic field mode in a cavity. The states of the two-level system are allowed to decay because of the interaction with the environment, and this is included phenomenologically in our non-Hermitian Hamiltonian by introducing complex energies for the fermion system. We focus our attention on the occurrence of exceptional points in the spectrum of the Hamiltonian, clarifying its mathematical and physical meaning