Hydrogen atom in monochromatic field: chaos and dynamical photonic localization

Casati, Giulio; Guarneri, Italo; Shepelyansky, Dima L.

doi:10.1109/3.982

Cited by 242 publications

(240 citation statements)

References 39 publications

Supporting

Mentioning

225

Contrasting

Unclassified

Order By: Relevance

“…The n 0 dependence of the dimensionless chaotic ionization rate γ/∆ is very different: it shows a slow, algebraic increase with n 0 . A simple analysis based on a Kepler map [131] description would yield a linear increase with n 0 , whereas our data seem to suggest a quadratic function of n 0 . This discrepancy is not very surprising, bearing in mind the simplicity of the Kepler map approach.…”

Section: Ionization Rates and Chaos Assisted Tunnelingcontrasting

confidence: 79%

“…Also the Fourier components of the unperturbed classical position operator r(t) are well known [131]. In the local coordinate system of the Kepler ellipse (motion in the (x ′ , y ′ ) plane, with major axis along x ′ ), one gets:…”

Section: Action-angle Coordinatesmentioning

confidence: 99%

“…This is due to the classical confinement of the electron inside the regular island. To ionize, the electron has no other option but to tunnel out of the classically confining island, before gaining energy by diffusive excitation [131]. The resonance island is strictly confining only for a one-dimensional system.…”

Section: Ionization Rates and Chaos Assisted Tunnelingmentioning

confidence: 99%

See 2 more Smart Citations

Non-dispersive wave packets in periodically driven quantum systems

2002

View full text Add to dashboard Cite

With the exception of the harmonic oscillator, quantum wave packets usually spread as time evolves. This is due to the non-linear character of the classical equations of motion which makes the various components of the wave packet evolve at various frequencies. We show here that, using the non-linear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the non-linear resonance island. We discuss the general mechanism which produces the non-dispersive wave packets, with emphasis on simple realization in the electronic motion of a Rydberg electron driven by a microwave field. We show the robustness of such wave packets for a model one-dimensional as well as for realistic three-dimensional atoms. We consider their essential properties such as the stability versus ionization, the characteristic energy spectrum and long lifetimes. The requirements for experiments aimed at observing such non-dispersive wave packets are also considered. The analysis is extended to situations in which the driving frequency is a multiple of the internal atomic frequency. Such a case allows us to discuss non-dispersive states composed of several, macroscopically separated wave packets communicating among themselves by tunneling. Similarly we briefly discuss other closely related phenomena in atomic and molecular physics as well as possible further extensions of the theory. (C) 2002 Elsevier Science B.V. All rights reserved

show abstract

Section: Ionization Rates and Chaos Assisted Tunnelingcontrasting

confidence: 79%

Section: Action-angle Coordinatesmentioning

confidence: 99%

Section: Ionization Rates and Chaos Assisted Tunnelingmentioning

confidence: 99%

See 1 more Smart Citation

Non-dispersive wave packets in periodically driven quantum systems

2002

View full text Add to dashboard Cite

show abstract

“…Our experimental system is a realization of the paradigmatic kicked rotor (KR) model [14,15], whose relevance lies in the fact that it shows the basic features of a complex dynamical system, and it may be used to locally (in energy) approximate much more complicated systems, such as microwave-driven Rydberg atoms [16], or an ion in a particle accelerator [1,17].…”

Section: Methodsmentioning

confidence: 99%

Experimental verification of a one-parameter scaling law for the quantum and “classical” resonances of the atom-optics kicked rotor

et al. 2005

View full text Add to dashboard Cite

We present experimental measurements of the mean energy in the vicinity of the first and second quantum resonances of the atom optics kicked rotor for a number of different experimental parameters. Our data is rescaled and compared with the one parameter ǫ-classical scaling function developed to describe the quantum resonance peaks. Additionally, experimental data is presented for the "classical" resonance which occurs in the limit as the kicking period goes to zero. This resonance is found to be analogous to the quantum resonances, and a similar one-parameter classical scaling function is derived, and found to match our experimental results. The width of the quantum and classical resonance peaks is compared, and their Sub-Fourier nature examined.

show abstract

“…We shall now assume that the reservoir is Markovian, i.e., the correlation functions (41) decay to zero on a time scale To much smaller than the typical time scales (43) of the master equation [see (49) below]. Then we may replace for T l<1±) (T -7-' ) = 27r8 (7 …”

Section: The First Term Under the Trace Vanishes Becausementioning

confidence: 99%

Dynamical localization in the microwave interaction of Rydberg atoms: The influence of noise

et al. 1991

View full text Add to dashboard Cite

We present experimental and theoretical results on highly excited Rydberg atoms passing through a waveguide. The waveguide is excited in a coherent mode with a superimposed component of technically generated noise. In the theoretical part of the paper we derive and solve a master equation for a Rydberg atom driven by a monochromatic coherent microwave field in the presence of noise. We show that a Rydberg atom subjected to a mixture of coherent modes and noise fields exhibits four dynamical regimes: (i) diffusive broadening, (ii) localization, (iii) destruction of coherence and localization, and (iv) relaxation to equilibrium. The four regimes are passed one after the other as a function of irradiation time. They occur on different time scales and are thus temporally well separated from each other. The theory is checked by an experiment on the time dependence of the population distribution of highly excited rubidium Rydberg atoms initially prepared in a unique and well-defined Rydberg state and irradiated by a strong microwave field. The localization regime, characterized by a "freezing" of the width of the wave packet with respect to the Rydberg levels, has been observed. The addition of a small noise component was shown to lead to delocalization after times inversely proportional to the noise power, as predicted by our theory. PACS number(s): 32.80. Rm, 05.45. +b,

show abstract

Hydrogen atom in monochromatic field: chaos and dynamical photonic localization

Cited by 242 publications

References 39 publications

Non-dispersive wave packets in periodically driven quantum systems

Non-dispersive wave packets in periodically driven quantum systems

Experimental verification of a one-parameter scaling law for the quantum and “classical” resonances of the atom-optics kicked rotor

Dynamical localization in the microwave interaction of Rydberg atoms: The influence of noise

Contact Info

Product

Resources

About