Transient localization in the kicked Rydberg atom

Abstract

We investigate the long-time limit of quantum localization of the kicked Rydberg atom. The kicked Rydberg atom is shown to possess in addition to the quantum localization time τ L a second cross-over time t D where quantum dynamics diverges from classical dynamics towards increased instability. The quantum localization is shown to vanish as either the strength of the kicks at fixed principal quantum number or the quantum number at fixed kick strength increases. The survival probability as a function of frequency in the transient localization regime τ L < t < t D is characterized by highly irregular, fractal-like fluctuations.

Multistability, Phase Diagrams and Statistical Properties of the Kicked Rotor: A Map With Many Coexisting Attractors

“…This remarkable feature was found to be true not only for regular but also in small-world, scale-free and other complex network structures, a novel and realistic framework that is attracting much attention in the literature at present [Newman et al, 2006;Watts, 1999;Jost, 2005;Barabási, 2003;Buchanan, 2002;Paula et al, 2006;Lind et al, 2004b]. A number of interesting related questions involving kicked rotors have been discussed recently [Chacon & García-Hoz, 2003;Wimberger, 2004;Persson et al, 2006].…”

Multiphoton population transfer in a kicked Rydberg atom: adiabatic rapid passage by separatrix crossing

“…Results of three-dimensional CTMC simulations including three more intermediate values of a are shown in figure 8 where we use a flat-top pulse envelope of ∼36 ns at the FWHM and F K = 2.5 V cm −1 . For cos 3 (ωt +ωt 2 ) pulses (a = 1), only about 5% transfer into n = 80 is achieved with a total of 40% of the population spreading over the n = 79-85 band. Larger and larger fraction of the population is transferred into n = 80 with narrower spread in final n as a is decreased.…”

“…This is termed dynamical localization and described by a mixed phase space picture where the atom is stable against ionization on one of a series of stable islands. In the long time limit, the atom eventually ionizes due to increased instability in the quantum mechanics which is absent in the classical picture [3]. Very different behaviour is observed when the atom is kicked bidirectionally [4].…”

“…Same as figure 11 but for two different peak field strengths of F K = 26 V cm −1 and F K = 39 V cm −1 for sin3 (ωt) 'kicked' atom using the 4-photon resonance condition. As in figure 11, driving the system harder destroys the stable structures above the main island creating a chaotic sea that extends high up in action.…”

Microwave-Driven Atoms: From Anderson Localization to Einstein’s Photoeffect

“…When a Hamiltonian quantum system is periodically driven and its classical counterpart undergoes a transition to chaotic diffusion, an analogous localization phenomenon occurs: destructive interference between many chaotically diffusing trajectories inhibits the transport and localizes the diffusing particle's wave function [3]. Since dynamical chaos rather than static disorder establish Anderson's scenario here, the phenomenon is often labeled dynamical localization.By now, the dynamical variant of Anderson localization (and similar phenomena [4]) was observed in a vast range of physical systems -ranging from cold atoms [5] to photon billiards [6] and atoms [7,8,9,10], and is best understood in the Floquet or dressed state picture, which also allows its formal mapping on Anderson's model [11]. The dressing of the bare system by the driving field photons defines multiphoton transition amplitudes between the initial and the final field-free state, mediated by nearresonantly coupled intermediate states.…”