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Physical Review A

Measurement of the electronic momentum distributions of Rydberg Stark states

Jeremy Murray-Krezan, R. R. Jones

Published Jun 8, 2007• 5 citations
Publisher

Abstract

Approximate momentum distributions of Rydberg electrons in static electric fields have been obtained using an improved impulsive momentum retrieval (IMR) technique. An imaging detector enables the measurement of half-cycle pulse (HCP) ionization probability across the spatial profile of a focused half-cycle pulse beam. By modulating the HCP amplitude we directly measure the derivative of the ionization vs HCP impulse curve, enabling the recovery of momentum distributions with better resolution than previously demonstrated with IMR. For example, for Stark states with small dipole moments, we observe predicted fine-structure in the projection of the momentum distribution along the Stark field axis. We use a semiclassical model to simulate the effect that the nonzero HCP duration has on our measurements. Good agreement between simulated and measured momentum distributions is obtained.

DOI
10.1103/physreva.75.063411

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Approximate momentum distributions of Rydberg electrons in static electric fields have been obtained using an improved impulsive momentum retrieval (IMR) technique. An imaging detector enables the measurement of half-cycle pulse (HCP) ionization probability across the spatial profile of a focused half-cycle pulse beam. By modulating the HCP amplitude we directly measure the derivative of the ionization vs HCP impulse curve, enabling the recovery of momentum distributions with better resolution than previously demonstrated with IMR. For example, for Stark states with small dipole moments, we observe predicted fine-structure in the projection of the momentum distribution along the Stark field axis. We use a semiclassical model to simulate the effect that the nonzero HCP duration has on our measurements. Good agreement between simulated and measured momentum distributions is obtained.
The characteristics of quasi-one-dimensional (1D) high-nnn Rydberg atoms produced by photoexciting, in a weak dc field, extreme members of the n=350n=350n=350 Stark manifold are investigated by studying their ionization when subjected to unidirectional electric field pulses, termed half-cycle pulses (HCP's), of duration Tp⪡Tn{T}_{p}⪡{T}_{n}Tp​⪡Tn​ where Tn{T}_{n}Tn​ is the classical electron orbital period, 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. It is shown that HCP's applied transverse to the atomic axis provide a particularly sensitive probe of the quasi-1D nature of the state. The experimental data are in good agreement with the results of classical trajectory Monte Carlo simulations.
The influence of the half-cycle pulse (HCP) kick on the asymptotic velocity of the ejected electron has been studied for excited xenon atoms (n∗=34){(n}^{*}=34)(n∗=34) in the presence of a static electric field $(220\mathrm{V}{\mathrm{cm}}^{\ensuremath{-}1}).$ We find that the HCP does not change the momentum distribution perpendicular to the kick direction. Therefore half-cycle pulse ionization and electron velocity map imaging can be used to obtain two-dimensional momentum distributions of atomic Rydberg states. Semiclassical and quantum mechanical calculations complement the experimental results.
Nearly unipolar, subpicosecond half-cycle pulses (HCPs) have been used to ionize Ba+{\mathrm{Ba}}^{+}Ba+ ngngng Rydberg ions. The double ionization probability vs HCP field strength data are compared with analogous single ionization measurements for neutral Ba 6snd6snd6snd Rydberg atoms prepared in the same apparatus. We find that neutral and ionic Rydberg states with the same binding energies follow approximately the same ionization curves. Our findings are in agreement with the predictions of an impulsive ionization model and classical trajectory Monte Carlo simulations.
We study the dynamics of highly excited (Rydberg) atoms in laboratory-scale magnetic fields via their ionization by THz half-cycle pulses (HCPs). A half-cycle pulse is a unipolar electromagnetic pulse that can probe an atomic electron at all points along its orbit around the atomic core. The dynamical evolution of diamagnetic Zeeman states subjected to an ultrashort (picosecond) HCP is calculated for both hydrogen and sodium atoms. Diamagnetic Zeeman states are localized parallel and perpendicular to the magnetic field. We use a grid-based pseudo-potential method to determine these eigenstates of the combined Coulomb-diamagnetic potential. We study states with principal quantum number n between 15--30 in the ℓ-mixing regime at magnetic fields of 1--6T. These initial states are subjected to the electric field of an HCP and their subsequent time evolution is calculated by solving the time-dependent Schrodinger equation. The HCP width is varied between the short pulse (impulsive) and the long pulse limit, keeping the total momentum transferred a constant. We calculate the total ionized fraction, and also the spectrum of the ionized photoelectrons. We find that, in the impulsive limit, where the width of the pulse is much smaller than typical time scales in the system, the calculated amount of ionization and the photoelectron spectra are different depending on the localization of the initial state. These differences are shown to be due to the different initial momentum distributions of the parallel and perpendicular states. As the duration of the HCP is made longer, we find that ionization is suppressed as compared with the impulsive limit. The states localized perpendicular to the magnetic field are found to be much more sensitive to the HCP width than the parallel states, reflecting the fact that the two classes of states interact with different parts of the Coulomb-diamagnetic potential during the HCP. The ionization characteristics are shown to scale classically with the principal quantum number. The results are presented in such a manner that they can be verified by experiment.
The asymptotic velocity distribution of electrons ionized in half-cycle-pulse excitation of high Rydberg states (n=34), placed in a static electric field, is studied using electron velocity-map imaging. At weak half-cycle pulse strengths, the electrons escape over the saddle point in the potential. For strong half-cycle pulses, the electrons are emitted in the direction of the field kick. The much slower and less intense half cycle of opposite polarity, which necessarily follows the main half-cycle pulse, strongly affects the momentum distribution and reduces the excess energy of the electrons significantly.
The ionization of potassium np Rydberg atoms with n∼388n\sim388n∼388 by pulsed unidirectional electric fields, termed half-cycle pulses (HCPs), with various well-characterized shapes (rectangular, triangular, and sawtooth) and durations $T\sb{p}$ comparable to the classical electron orbital period $T\sb{n}$ is investigated. The experimental results are compared to classical trajectory Monte Carlo (CTMC) simulations and the classically-scaled results of quantum calculations undertaken at n=5.n=5.n=5. The data show that in the intermediate regime, $T\sb{p}\sim T\sb{n},$ the threshold field for ionization becomes sensitive to the shape and rise time of the HCP, increasing with increasing rise time. For each pulse shape, the agreement between the experimental measurements and both the CTMC and quantum calculations is very good.