We study the three-dimensional (3D) unidirectionally kicked Rydberg atom. For parabolic initial states elongated in the direction of the kicks we show that the ionization of the quantum system is suppressed as compared to the classical counterpart and that the quantum wave function is localized along all degrees of freedom, whereas the classical system is globally diffusive. We discuss the connection to the previously studied one-dimensional (1D) model of the kicked Rydberg atom and verify that the 1D model is a good approximation to the 3D quantum case in the limiting case of the most elongated initial states. We further study the quantum phase-space distribution (Husimi distribution) of the eigenstates of the period-one time-evolution (Floquet) operator and show that the eigenstates are localized in phase space. For the most elongated parabolic initial state, we are able to identify the unstable periodic orbits around which Floquet states localize. We discuss the possibility of observing quantum localization in high Rydberg states in $ng100.$ We study the three-dimensional (3D) unidirectionally kicked Rydberg atom. For parabolic initial states elongated in the direction of the kicks we show that the ionization of the quantum system is suppressed as compared to the classical counterpart and that the quantum wave function is localized along all degrees of freedom, whereas the classical system is globally diffusive. We discuss the connection to the previously studied one-dimensional (1D) model of the kicked Rydberg atom and verify that the 1D model is a good approximation to the 3D quantum case in the limiting case of the most elongated initial states. We further study the quantum phase-space distribution (Husimi distribution) of the eigenstates of the period-one time-evolution (Floquet) operator and show that the eigenstates are localized in phase space. For the most elongated parabolic initial state, we are able to identify the unstable periodic orbits around which Floquet states localize. We discuss the possibility of observing quantum localization in high Rydberg states in $ng100.$

APSMay 1, 20030 citations

Semiclassical analysis of quantum localization of the periodically kicked Rydberg atom

S. Yoshida, Frank Großmann, Emil Persson +1 more

The periodically kicked Rydberg atom displays quantum localization, features of which depend on the orientation and strength of the unidirectional kicks. They include scarring of the wave function, localization by cantori, and exponential localization in the regime of strong perturbation resembling dynamical localization. Using the semiclassical Herman-Kluk propagator we investigate the degree to which semiclassical dynamics can mimic quantum localization. While the semiclassical approximation has difficulties to reproduce the scarred wave functions, the exponential tail which is a typical signature of the dynamical localization is well represented in the case of strong classical diffusion. Also the localization by broken tori is observed in the semiclassical recurrence probability for short times but the deviation from the corresponding quantum dynamics becomes more pronounced for the long-time evolution.The periodically kicked Rydberg atom displays quantum localization, features of which depend on the orientation and strength of the unidirectional kicks. They include scarring of the wave function, localization by cantori, and exponential localization in the regime of strong perturbation resembling dynamical localization. Using the semiclassical Herman-Kluk propagator we investigate the degree to which semiclassical dynamics can mimic quantum localization. While the semiclassical approximation has difficulties to reproduce the scarred wave functions, the exponential tail which is a typical signature of the dynamical localization is well represented in the case of strong classical diffusion. Also the localization by broken tori is observed in the semiclassical recurrence probability for short times but the deviation from the corresponding quantum dynamics becomes more pronounced for the long-time evolution.

Physical Review AApr 28, 200420 citations

Quantum localization in the high-frequency limit

Emil Persson, S. Yoshida, Xiao‐Min Tong +2 more

The quantum localization of the periodically kicked Rydberg atom in the limit of high frequencies $\ensuremath{\nu}$ is studied. We show that the quantum suppression of fast chaotic ionization as predicted by classical dynamics persists as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nu}}\ensuremath{\infty}.$ Properties of localization in the regime of strong coupling to the continuum due to one-photon transitions are discussed. For the unidirectionally kicked atom, the high-frequency limit of localization is determined by the zero-frequency Stark Hamiltonian. The persistence of quantum localization due to interference of classical trajectories can be understood in terms of smearing out of the instabilities at finite $\ensuremath{\Elzxh}.$ Unstable trajectories whose action differs from each other and from Stark orbits in less than $\ensuremath{\Elzxh}$ contribute to quantum localization rather than to chaotic ionization.The quantum localization of the periodically kicked Rydberg atom in the limit of high frequencies $\ensuremath{\nu}$ is studied. We show that the quantum suppression of fast chaotic ionization as predicted by classical dynamics persists as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nu}}\ensuremath{\infty}.$ Properties of localization in the regime of strong coupling to the continuum due to one-photon transitions are discussed. For the unidirectionally kicked atom, the high-frequency limit of localization is determined by the zero-frequency Stark Hamiltonian. The persistence of quantum localization due to interference of classical trajectories can be understood in terms of smearing out of the instabilities at finite $\ensuremath{\Elzxh}.$ Unstable trajectories whose action differs from each other and from Stark orbits in less than $\ensuremath{\Elzxh}$ contribute to quantum localization rather than to chaotic ionization.

Physical Review AOct 10, 20027 citations

Floquet analysis of the dynamical stabilization of the kicked hydrogen atom

S. Yoshida, Carlos O Reinhold, Peter Kristöfel +3 more

We analyze the quantum dynamics of the one-dimensional periodically kicked Rydberg atom. The time-dependent Schr\"odinger equation is solved by employing a nonunitary representation of the period-one evolution operator in a finite basis set that accounts for the outbound probability flux. We find a direct correspondence between stable classical islands in phase space and the quantum Husimi distributions of stable Floquet states. These results explain the pronounced peak recently found experimentally in the frequency-dependent survival probability of Rydberg states subject to a sequence of half-cycle pulses.We analyze the quantum dynamics of the one-dimensional periodically kicked Rydberg atom. The time-dependent Schr\"odinger equation is solved by employing a nonunitary representation of the period-one evolution operator in a finite basis set that accounts for the outbound probability flux. We find a direct correspondence between stable classical islands in phase space and the quantum Husimi distributions of stable Floquet states. These results explain the pronounced peak recently found experimentally in the frequency-dependent survival probability of Rydberg states subject to a sequence of half-cycle pulses.

Physical Review AJun 1, 199917 citations

Pulse-induced focusing of Rydberg wave packets

D. G. Arbó, Carlos O Reinhold, Joachim Burgdörfer +5 more

We demonstrate that strong transient phase-space localization can be achieved by the application of a single impulsive ``kick'' in the form of a short (600 ps) unidirectional electric-field pulse to a strongly polarized, quasi-one-dimensional Rydberg atom. The underlying classical dynamics is analyzed and it is shown that phase-space localization results from a focusing effect analogous to rainbow scattering. Moreover, it is shown that the essential features of the classical analysis remain valid in a quantum-mechanical treatment of the system in terms of its phase-space Husimi distribution. The degree of phase-space localization is characterized by the coarse-grained Renyi entropy. Transient phase-space localization is demonstrated experimentally using extreme redshifted $m=0$ potassium Stark states in the $n=351$ manifold and a short probe pulse. The experimental data are in good agreement with theoretical predictions. The localized state provides an excellent starting point for further control and manipulation of the electron wave packet.We demonstrate that strong transient phase-space localization can be achieved by the application of a single impulsive ``kick'' in the form of a short (600 ps) unidirectional electric-field pulse to a strongly polarized, quasi-one-dimensional Rydberg atom. The underlying classical dynamics is analyzed and it is shown that phase-space localization results from a focusing effect analogous to rainbow scattering. Moreover, it is shown that the essential features of the classical analysis remain valid in a quantum-mechanical treatment of the system in terms of its phase-space Husimi distribution. The degree of phase-space localization is characterized by the coarse-grained Renyi entropy. Transient phase-space localization is demonstrated experimentally using extreme redshifted $m=0$ potassium Stark states in the $n=351$ manifold and a short probe pulse. The experimental data are in good agreement with theoretical predictions. The localized state provides an excellent starting point for further control and manipulation of the electron wave packet.

Physical Review AJun 13, 200362 citations

The kicked atom: Characterization of quasi-one-dimensional Rydberg atoms and their nonlinear dynamics

Zhao, Wei

The characteristics of strongly-polarized quasi-one-dimensional (quasi-1D) Rydberg atoms produced by photoexcitation of selected Stark states in the n = 350 Stark manifold are investigated by studying their ionization when subject to sub-nanosecond unidirectional electric field pulses, termed half-cycle pulses (HCPs), directed both parallel and perpendicular to the atomic axis. The observed differences in the ionization characteristics provide a measure of the anisotropy of the momentum distribution and thus of the quasi-1D nature of the states. The response of such states to a train of HCPs directed parallel and anti-parallel to the axis of polarization of the initial state is also investigated. Pronounced differences in the survival probability are observed confirming theoretical predictions that the dynamical response of the system will be very different for these two conditions. The presence of noise is also observed to play a crucial role in the dynamics. Reasonable agreement between experiment and theory is achieved.The characteristics of strongly-polarized quasi-one-dimensional (quasi-1D) Rydberg atoms produced by photoexcitation of selected Stark states in the n = 350 Stark manifold are investigated by studying their ionization when subject to sub-nanosecond unidirectional electric field pulses, termed half-cycle pulses (HCPs), directed both parallel and perpendicular to the atomic axis. The observed differences in the ionization characteristics provide a measure of the anisotropy of the momentum distribution and thus of the quasi-1D nature of the states. The response of such states to a train of HCPs directed parallel and anti-parallel to the axis of polarization of the initial state is also investigated. Pronounced differences in the survival probability are observed confirming theoretical predictions that the dynamical response of the system will be very different for these two conditions. The presence of noise is also observed to play a crucial role in the dynamics. Reasonable agreement between experiment and theory is achieved.

Jan 1, 20050 citations

n>100.

ng100.

m=0

potassium Stark states in the

n=351

manifold and a short probe pulse. The experimental data are in good agreement with theoretical predictions. The localized state provides an excellent starting point for further control and manipulation of the electron wave packet.