Short Half-cycle Pulses Research Articles

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.

Ionization of the hydrogen atom by short half-cycle pulses: dependence on the pulse duration

A theoretical study of the ionization of hydrogen atoms by short external half-cycle pulses (HCPs) as a function of the pulse duration, using different quantum and classical approaches, is presented. Total ionization probability and energy distributions of ejected electrons are calculated in the framework of the singly-distorted Coulomb-Volkov (SDCV) and the doubly-distorted Coulomb-Volkov (DDCV) approximations. We also performed quasiclassical calculations based on a classical trajectory Monte Carlo method which includes the possibility of tunneling (CTMC-T). Quantum and classical results are compared to the numerical solution of the time-dependent Schrodinger equation (TDSE). We find that for high momentum transfers the DDCV shows an improvement compared to the SDCV, especially in the low-energy region of the electron emission spectra, where SDCV fails. In addition, DDCV reproduces successfully the TDSE electron energy distributions at weak momentum transfers. CTMC-T results reveal the importance of tunneling in the ionization process for relative long pulses and strong momentum transfers but fails to overcome the well-known classical suppression observed for weak electric fields.

Electron beam from oriented Rydberg atoms irradiated by a half-cycle pulse

The angular and energy distributions of electrons emitted from Rydberg atoms prepared in the extreme Stark state and irradiated by a short half-cycle pulse are calculated in the framework of quantum-mechanical and semiclassical theories. It is supposed that the pulse direction coincides with the direction of orientation of atoms. The emitted electrons are concentrated in a small angle around the direction of orientation of the Rydberg atoms. Semiclassical theory shows that the width of the angular distribution scales as 1/qn3/2 and decreases with increase of either the principal quantum number n of the initial state or the momentum q transferred to the electron.

Electron stripping and reattachment at atomic centers using attosecond half-cycle pulses

We investigate the response of two three-body Coulomb systems when driven by attosecond half-cycle pulses: The electron transfer between two hydrogen atomic centers and the double ionization of the helium atom. Using very short half-cycle pulses (HCPs) which effectively deliver ``kicks'' to the electrons, we first study how a carefully chosen sequence of HCPs can be used to control to which of one of the two fixed atomic centers the electron gets reattached (HCP assisted electron transfer). Moving from one electron in two atomic centers to two electrons in one atomic center we then study the double ionization from the ground state of He by a sequence of attosecond time-scale HCPs, with each electron receiving effectively a ``kick'' from each HCP. We investigate how the net electric field of the sequence of HCPs affects the total and differential ionization probabilities.

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.

Modulation and correlation of the radial and angular motions of a Rydberg electron in a resonance microwave field

We discuss the physical sense and interpretation of the Maeda—Gallagher experiment (2004) in which the probability of ionisation of Rydberg Li atoms perturbed by the resonance microwave field by a short half-cycle pulse was measured. The periodic dependence of the ionisation probability wi on the delay time t0 of the half-cycle pulse with respect to the instant of switching on the microwave field is found. The oscillation period of the function wi(t0) is equal to the Kepler period of a Rydberg electron. It is shown that the interpretation of this experiment by the authors in terms of localised wave packets has no grounds and neglects basic processes proceeding in the microwave field. An alternative interpretation is proposed and, as the first step, the structure of the Rydberg wave function formed in the resonance microwave field is studied.

Bidirectionally kicked Rydberg atoms: Population trapping near the continuum

The behavior of high-n Rydberg atoms subject to a periodic sequence of short half-cycle pulses (HCPs) that alternate in sign is reexamined. Each HCP delivers an impulsive momentum transfer or 'kick' to the electron and the net average field it experiences is zero. The data show that the excited electron energy distribution initially moves toward the continuum, i.e., toward states of higher n, but then becomes transiently trapped near the edge of the continuum leading to sizable overall survival probabilities. The physical mechanisms responsible for this are discussed with the aid of classical trajectory Monte Carlo simulations.

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.

Large angular-momentum changing in a short half-cycle pulse interaction with a Rydberg atom

We show that, in contrast to multiphoton absorption in atoms, the remote region from a nucleus is dominant in the process of a half-cycle pulse interaction with a Rydberg atom, and that this interaction produces a very large change in the angular momentum of the electron. We have found good agreement between classical trajectory Monte Carlo, semiclassical, and quantum-mechanical calculations for the energy distribution of the electron.

Excitation and ionization of Rydberg atoms by short half-cycle pulses

Simple semiclassical formulas are derived for the probability of excitation and ionization of Rydberg atoms irradiated by a half-cycle pulse whose duration is shorter than the Kepler period. The calculated ionization probabilities are in good agreement with the experimental data of Jones, You, and Bucksbaum [Phys. Rev. Lett. 70, 1236 (1993)] and with previous calculations.

Accurate ionization thresholds of atoms subject to half-cycle pulses

The evolution of Rydberg states of hydrogen and alkali-metal atoms subject to short half-cycle pulses is studied. The convergence of the numerical solutions of the time-dependent Schrodinger equation based on an expansion of the electronic wave function in a finite basis set of Sturmian functions is analyzed in detail. It is shown that the accuracy of such calculations can be established by investigating the stabilization of the transition probabilities with respect to the parameters that define the basis set. The dependence of the quantum and classical ionization thresholds on the pulse shape is investigated. The calculations are compared with experimental data for various pulse profiles, which feature slow or fast rise times. The results show that the ionization thresholds for long pulses are very sensitive to the rise time of the electric field. @S1050-2947~98!00309-6# PACS number~s!: 32.80.Rm, 02.60.2x During the last few years, the ionization and excitation of Rydberg atoms by pulsed unidirectional electric fields, termed half-cycle pulses ~HCPs!, have been investigated ex- tensively. Experiments have reached the regime in which the effective duration of the pulses T p and the peak fieldsFp are of the order of the classical electron orbital period Tni 52pn i and the Coulomb electric field Fn i 5n i4 in the

Creating and probing coherent atomic states

We present a brief review of recent experimental and theoretical time-resolved studies of the evolution of atomic wavepackets, in particular, wavepackets comprising a superposition of very-high-lying Rydberg states that are created either using a short half-cycle pulse (HCP) or by rapid application of a DC field. The properties of the wavepackets are probed using a second HCP that is applied following a variable time delay and which ionizes a fraction of the atoms, much like a passing-by ion in atomic collisions.