Kicked Rydberg Atom Research Articles

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

Following an experimental observation, a recent simulation has shown that efficient population transfer can be achieved through adiabatic chirping of a microwave pulse through a 10-photon resonance connecting two Rydberg states with n = 72, ℓ = 1 and n ∼ 82. These simulations have revealed that this population transfer is essentially a classical transition caused by separatrix crossing in the classical phase space. Here, we present the results of our fully three-dimensional quantum and classical simulations of coherent multiphoton population transfer in a kicked Li atom in a Rydberg state. We were able to achieve ∼76% population transfer from the 40p to 46p state in Li through a 6-photon resonance and contrast our results with those when the transition is driven by microwaves. We further discuss the case when the atom starts out from a Stark state in conjunction with the ℓ-distribution of the transferred population. We use a one-dimensional classical model to investigate the classical processes taking place in the phase space and find that the same separatrix crossing mechanism observed in microwave transitions is also responsible for the transition when the atom is kicked.

Transient localization in the kicked Rydberg atom

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 $\tau_L$ 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 $\tau_L<t<t_D$ is characterized by highly irregular, fractal-like fluctuations.

Virtual photon effects on classical chaos in a periodically kicked Rydberg atom system

We study classical chaos in the system of a two-level Rydberg atom interacting with a pulsed standing microwave. This model approaches the form of an atom optics realization of a usual delta-kicked rotor under the rotating-wave approximation (RWA). We find that the non-energy-conserving processes or virtual photon processes neglected in the RWA have a strong effect on the classical chaos, which can enhance, reduce and even completely suppress the chaos under certain kicked conditions. The system displays non-KAM dynamical behavior for rational and irrational kicks.

Non-energy-conserving effects on dynamical localization in a periodically kicked Rydberg atom

We study the dynamical localization in the system of a two-level Rydberg atom interacting exactly with a pulsed standing microwave. This system approaches an atom optics realization of usual delta-kicked rotor under the rotating-wave approximation (RWA). We find that the non-energy-conserving processes neglected in the RWA have a strong effect on the classical and quantum diffusion, which, compared with the results of the RWA, can enhance, reduce and even completely suppress the momentum diffusion under certain kicked conditions.

Semiclassical analysis of quantum localization of the periodically kicked Rydberg atom

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.

Quantum localization in the three-dimensional kicked Rydberg atom

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 $ng100.$

The Kicked Rydberg Atom: A New Laboratory for Study of Non-linear Dynamics

Recent advances in experimental technique have enabled the study of atoms subject to impulsive perturbations of duration Tp << Tn, where Tn is the classical electron orbital period. Such “kicked” atoms provide new opportunities for the control and manipulation of atomic wavefunctions and for the investigation of non-linear dynamics in Hamiltonian systems. Here we discuss the rich variety of dynamical behaviors that are observed and their physical origins, together with several possible avenues for future research.

Quantum localization in the high-frequency limit

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.

Kicked Rydberg atom: Response to trains of unidirectional and bidirectional impulses

The behavior of $\mathrm{Rb}(390p)$ atoms subject to a train of up to 50 half-cycle pulses (HCPs) with duration ${T}_{p}\ensuremath{\ll}{T}_{n},$ where ${T}_{n}$ is the classical electron orbital period, is investigated. In this limit, each HCP simply delivers an impulsive momentum transfer or ``kick'' to the electron. The response of atoms to a series of unidirectional kicks and to a series of kicks that alternate in direction is compared. For unidirectional kicks, the Rydberg atom survival probability has a pronounced maximum when the pulse repetition frequency ${v}_{p}$ is \ensuremath{\sim}1.3 times the classical orbital frequency ${v}_{n}.$ Classical simulations show this behavior provides a signature of dynamical stabilization. Evidence of dynamical stabilization and chaotic diffusion is also found in the distribution of final bound states. Very different behavior is observed for alternating kicks. The survival probability generally increases with ${v}_{p},$ although a small local maximum is evident when ${v}_{p}\ensuremath{\sim}{v}_{n}.$ Little evidence of dynamical stabilization is observed in either the calculated dependence of the survival probability on the number of applied kicks, in the measured final bound-state distribution, or in the classical phase space of the kicked atom. Model calculations for a one-dimensional ``atom'' reveal islands of stability, but their three-dimensional counterparts are found to be unstable.

Exponential and nonexponential localization of the one-dimensional periodically kicked Rydberg atom

We investigate the quantum localization of the one-dimensional Rydberg atom subject to a unidirectional periodic train of impulses. For high frequencies of the train the classical system becomes chaotic and leads to fast ionization. By contrast, the quantum system is found to be remarkably stable. We identify for this system the coexistence of different localization mechanisms associated with resonant and nonresonant diffusion. We find for the suppression of nonresonant diffusion an exponential localization whose localization length can be related to the classical dynamics in terms of the ``scars'' of the unstable periodic orbits. We show that the localization length is determined by the energy excursion along the periodic orbits. The suppression of resonant diffusion along the sequence of photonic peaks is found to be nonexponential due to the presence of high harmonics in the driving force.

Quantum Localization of the Kicked Rydberg Atom

We investigate the quantum localization of the one-dimensional Rydberg atom subject to a unidirectional periodic train of impulses. For high frequencies of the train the classical system becomes chaotic and leads to fast ionization. By contrast, the quantum system is found to be remarkably stable. We find this quantum localization to be directly related to the existence of "scars" of the unstable periodic orbits of the system. The localization length is given by the energy excursion along the periodic orbits.

Floquet analysis of the dynamical stabilization of the kicked hydrogen atom

We analyze the quantum dynamics of the one-dimensional periodically kicked Rydberg atom. The time- dependent Schrodinger equation is solved by employing a nonunitary representation of the period-one evolu- tion operator in a finite basis set that accounts for the outbound probability flux. We find a direct correspon- dence 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. @S1050-2947~99!50606-9#

Dynamical Stabilization of the Periodically Kicked Rydberg Atom

Measurements in which $K(\mathrm{np})$ Rydberg atoms with $n\ensuremath{\sim}388$ are subject to a train of up to 50 half-cycle pulses are reported and reveal a peak in the atomic survival probability for pulse repetition frequencies near the classical orbital frequency. Classical calculations show that this behavior is associated with dynamical stabilization and the periodic orbits in phase space around which stable islands form are identified. This work provides the first direct evidence for dynamical stabilization of a periodically kicked Rydberg atom.

The kicked rydberg atom: Regular and stochastic motion

We have investigated the dynamics of a three-dimensional classical Rydberg atom driven by a sequence of pulses. Both the deterministic system with periodic pulses and the closely related “noisy” system with random pulses have been studied in parallel. The Lyapunov exponent is calculated as a function of pulse height and the angular momentum of the initial state. We find differences between noisy and deterministic perturbations to be most pronounced for small pulse heights. Low angular momentum orbits show enhanced diffusion in agreement with recent experimental data for ion-solid interaction.