One-dimensional Rydberg Atom Research Articles

Dynamical stabilization of the initial state in a periodically kicked three-dimensional Rydberg atom

We present the dynamical stabilization of the initial state of a three-dimensional Rydberg atom subjected to a periodic train of half-cycle pulses. It is shown as an existence of a broad maximum of the survival probability at train repetition frequencies close to the classical orbital frequency. Population of the initial state for train repetition frequencies from this plateau is almost constant, even for trains consisting of a large number of pulses. We find this phenomenon very well observable for the initial redshifted Stark states. It is shown that for initial states with high and intermediate values of the angular quantum number, the dynamical stabilization of the initial state occurs only partially. We show that for extreme members of the Stark manifold as the initial states, results are fully consistent with appropriate results for a one-dimensional Rydberg atom.

Fractional Revival of Rydberg Wave Packets in Twice-Kicked One-Dimensional Atoms

We study revival and fractional revival phenomena of wave packets in a one-dimensional Rydberg atom irradiated by two time-delayed half-cycle pulses using an autocorrelation function characterized by electronic transition probabilities as weighting factors rather than modeling them by a Gaussian or Lorentzian distribution. If the momentum (q2) delivered to the atom by the second kick is much smaller than that (q1) imparted by the first one, the times of revival and fractional revival coincide with those of the single kicked atom. For q2 ≥ q1 4 appearance of revival and fractional revival depends on both the values of q2 and time delay t1 between the pulses but more sensitively on t1. The number of fractional revivals tends to become numerous as the value of t1 increases.

Electron Rydberg wave packets in one-dimensional atoms

An expression for the transition probability or form factor in one-dimensional Rydberg atom irradiated by short half-cycle pulse was constructed. In applicative contexts, our expression was found to be more useful than the corresponding result given by Landau and Lifshitz. Using the new expression for the form factor, the motion of a localized quantum wave packet was studied with particular emphasis on its revival and super-revival properties. Closed form analytical expressions were derived for expectation values of the position and momentum operators that characterized the widths of the position and momentum distributions. Transient phase-space localization of the wave packet produced by the application of a single impulsive kick was explicitly demonstrated. The undulation of the uncertainty product as a function of time was studied in order to visualize how the motion of the wave packet in its classical trajectory spreads throughout the orbit and the system becomes nonclassical. The process, however, repeats itself such that the atom undergoes a free evolution from a classical, to a nonclassical, and back to a classical state.

Dynamical stabilization of the initial state in a periodically kicked one-dimensional Rydberg atom

We investigate the dynamical stabilization of the initial state of a one-dimensional Rydberg atom subjected to a periodic train of half-cycle pulses. A survival probability of the initial state as a function of pulse repetition frequency is presented for different values of momentum transferred to the electron. This survival probability exhibits a broad maximum at train repetition frequencies close to the classical orbital frequency provided that the momentum is negative. There is no such behaviour for positive momentum transferred to the electron.

Analysis of Revival Phenomenon for Strong-Field Excitation of Rydberg Atom

Analysis of Revival Phenomenon for Strong-Field Excitation of Rydberg AtomThe autocorrelation function for a one-dimensional Rydberg atom irradiated by half-cycle pulse (HCP) is investigated. At weak field only the full revival is observed, at a medium field strength - a fractional revival, whereas at a strong field (when the continuous energy states are also populated) the revival phenomenon disappears. The contribution of the continuous energy states in the autocorrelation function decreases dramatically with time after the wave packet formation.

Wave packet fractional revivals in a one-dimensional Rydberg atom

We investigate many characteristic features of revival and fractional revival phenomena via derived analytic expressions for an autocorrelation function of a one-dimensional Rydberg atom with weighting probabilities modelled by a Gaussian or a Lorentzian distribution. The fractional revival phenomenon in the ionization probabilities of a one-dimensional Rydberg atom irradiated by two short half-cycle pulses is also studied. When many states are involved in the formation of the wave packet, the revival is lower and broader than the initial wave packet and the fractional revivals overlap and disappear with time.

Revival of ionization probability for a twice kicked 1D Rydberg atom

The ionization probability for a one-dimensional (1D) Rydberg atom interacting with two short half-cycle pulses is calculated as a function of the time delay between them. The impulse and semiclassical approximations are used. The ionization probability oscillates with a Kepler period around some constant value evaluated analytically too. The oscillations exhibit the quantum-mechanical revival and depend on the orientation of the momentum transfer and the principal quantum number of the initial state.

Analytical investigation of one-dimensional Rydberg atoms interacting with half-cycle pulses

Classical, quantum-mechanical, and semiclassical expressions for the transition probability in one-dimensional Rydberg atom irradiated by short half-cycle pulse are derived and compared. The simple formulas obtained for excitation of Rydberg atom by two time delayed weak half-cycle pulses reproduce well the experimental data and the solutions of time-dependent Schr\"odinger equation. When the transferred momenta are stronger and positive, the transition probabilities exhibit fast oscillations with time delay between the pulses. The classical transition probability is constant in time. For negative transferred momenta a focusing phenomenon is observed, and there is a region in time delay, where the transition probabilities oscillate with the Kepler period.

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.

Electrons above a helium surface and the one-dimensional Rydberg atom

Isolated electrons resting above a helium surface are predicted to have a bound spectrum corresponding to a one-dimensional hydrogen atom. But in fact, the observed spectrum is closer to that of a quantum-defect atom. Such a model is discussed and solved in analytic closed form.

Controlled suppression of ionization of Rydberg atoms in a microwave field

A computational procedure for controlling the stochastic ionization of one-dimensional single electron Rydberg atoms in the correspondence principle regime is developed. Using our procedure it is possible to suppress excitation and ionization of the one-dimensional Rydberg atom even in strong microwave fields for which ionization would otherwise be instantaneous.

Semiclassical treatment of a half-cycle pulse acting on a one-dimensional Rydberg atom.

The final-state distribution of hydrogen, acted upon by a 1/2-cycle pulse, has been calculated semiclassically for a proposed one-dimensional experiment. This work was motivated by the recent experimental realization of half-cycle pulses by Jones, You, and Bucksbaum [Phys. Rev. Lett. 70, 1236 (1993)] in which preliminary studies of ionization and state redistribution for hydrogenlike atoms were carried out. To simplify the situation theoretically, an experiment is proposed in which an additional weak static electric field is imposed and approximately one-dimensional states are selected. Within this one-dimensional approximation the transition probability to various n states (n is the principal quantum number) has been calculated as a function of the amplitude of the half-cycle pulse, using a semiclassical formula due to Miller [Adv. Chem. Phys. 25, 69 (1974)]. A complete derivation of this formula and a discussion of approximations are made in the following paper. We have found that an even number of trajectories always contributes to the transition probability and leads to observable interference effects. In addition, we find that bifurcations of these trajectories can occur, resulting in resonances and more complicated interference structures.

Half-cycle pulse acting on a one-dimensional Rydberg atom: Semiclassical transition amplitudes in action and angle variables.

In this paper we derive the expression for the transition coefficient used in the preceding paper [C. D. Schwieters and J. B. Delos, Phys. Rev. A 51, 1023 (1995)] for principal-quantum-number transitions in one-dimensional hydrogen caused by half-cycle pulses. We briefly review the methods of Miller [Adv. Chem. Phys. 25, 69 (1974)] and Marcus [Chem. Phys. Lett. 7, 525 (1970); J. Chem. Phys. 54, 3965 (1971)], and then derive the result using the methods of Maslov and Fedoriuk [[ital Semi]-[ital Classical] [ital Approximation] [ital in] [ital Quantum] [ital Mechanics], (Reidel, Dordrecht, 1981)]. Also, we examine the approximate reduction of hydrogen from three to one dimension and we find a hitherto unknown correction due to the residual motion of one of the ignored degrees of freedom. We discuss the regime of validity of this one-dimensional approximation.