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arXiv:physics/9812010 · Journal of Physics B Atomic Molecular and Optical Physics

Ionization dynamics in intense pulsed laser radiation. Effects of frequency chirping

Roberta Marani, E J Robinson

Published Jan 1, 1999• 11 citations
arXivHTMLPDF

Abstract

Via a non-perturbative method we study the population dynamics and photoelectron spectra of Cs atoms subject to intense chirped laser pulses, with Gaussian beams. We include above threshold ionization spectral peaks. The frequency of the laser is near resonance with the 6s-7p transition. Dominant couplings are included exactly, weaker ones accounted for perturbatively. We calculate the relevant transition matrix elements, including spin-orbit coupling. The pulse is taken to be a hyperbolic secant in time and the chirping a hyperbolic tangent. This choice allows the equations of motions for the probability amplitudes to be solved analytically as a series expansion in the variable , where is a measure of the pulse length. We find that the chirping changes the ionization dynamics and the photoelectron spectra noticeably, especially for longer pulses of the order of au. The peaks shift and change in height, and interference effects between the 7p levels are enhanced or diminished according to the amount of chirping and its sign. The integrated ionization probability is not strongly affected.

DOI
10.1088/0953-4075/32/3/014

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Via a non-perturbative method we study the population dynamics and photoelectron spectra of Cs atoms subject to intense chirped laser pulses, with Gaussian beams. We include above threshold ionization spectral peaks. The frequency of the laser is near resonance with the 6s-7p transition. Dominant couplings are included exactly, weaker ones accounted for perturbatively. We calculate the relevant transition matrix elements, including spin-orbit coupling. The pulse is taken to be a hyperbolic secant in time and the chirping a hyperbolic tangent. This choice allows the equations of motions for the probability amplitudes to be solved analytically as a series expansion in the variable , where is a measure of the pulse length. We find that the chirping changes the ionization dynamics and the photoelectron spectra noticeably, especially for longer pulses of the order of au. The peaks shift and change in height, and interference effects between the 7p levels are enhanced or diminished according to the amount of chirping and its sign. The integrated ionization probability is not strongly affected.
Abstract The effects of pulse chirping on the excitation and ionization process in hydrogen atoms are theoretically investigated by numerically solving the full time-dependent Schrödinger equation with a pseudospectral method. We specifically compare the dynamical results of single-photon resonant ionization (SRI) and two-photon resonant ionization (TRI) across laser intensities ranging from 10 12 to 10 14 W cm 2 . The ionization probabilities of SRI and TRI tend to exhibit opposite chirp dependent behaviors as the laser field changes from weak to strong, which are elucidated with the strong field approximation theory. Furthermore, the sensitivity of ionization probability to chirp can be suppressed at specific laser intensities when the laser field is synthesized by two-color resonant chirped pulses. Our study provides a basis for theoretical investigations into chirp effect on atomic photoionization, offering new insights into the coherent control of electron dynamics.
The dynamics of the bound-state populations and the photoelectron spectra are calculated for model atomic systems irradiated by a pulse with a harmonically modulated frequency. For a system including a single bound state a model is adopted, which takes into account the threshold behavior typical of negative ions and admits continuum-continuum transitions. For a model one-dimensional atom the results are obtained through a numerical integration of the Schr\"odinger equation. The case of a resonant ionization is also considered. The modulation of the frequency results in changing the instantaneous rate of decay of the initial state, in inducing additional population oscillations for multilevel systems, and in additional peaks in the photoelectron spectra.
In this project I developed a general method of finding the optimal laser excitation for an ensemble of two-level atoms with the primary goal of exciting as many atoms as possible, as quickly as possible, for as long as possible, in order of decreasing priority. Specifically, I simulated the laser excitation of a collection of Rubidium-87 atoms from (n=5, L=0, S=1/2, J=1/2) to (n=5, L=1, S=1/2, J=3/2), by finding numerical solutions to the optical Bloch equations. I optimized the parameters of a linear chirp paired with a Gaussian intensity pulse first neglecting and then including spontaneous emission, and then for a hyperbolic-tangent chirp paired with a squared-hyperbolic-secant intensity pulse including spontaneous emission. Comparing the optimal parameters for the linear chirp both with and without spontaneous emission demonstrated that neglecting spontaneous emission will lead to significant errors, at least when considering Rubidium-87. Comparing the linear chirp to the hyperbolic-tangent chirp (both with spontaneous emission) showed that both chirp shapes lead to excitation of greater than 96% of the population, and that based on my simulations, the linear chirp was slightly better at meeting all three goals of ceiling, speed and endurance. The best of all the excitations that I found using a linear chirp is to use a chirp rate between 0.2 and 0.65 GHz/ns and to use a pulse with a FWHM of 100 ns and a peak intensity of 10 W/cm^2.
Doppler-free population inversion induced by coherent two-photon resonance is calculated analytically for a two-photon analog of the hyperbolic-secant pulse and numerically for a Gaussian, linearly chirped pulse. The numerical calculations are carried out for a two-photon resonance of a chirped ruby laser line with the $6{S}_{\frac{1}{2}}\ensuremath{\rightarrow}9{D}_{\frac{3}{2}}$ transition in Cs. Complete inversion is found when the fractional change in frequency during the pulse lies between 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ and 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$. The coherent two-photon resonances are described by optical Bloch equations which are derived from a multiple-time-scale perturbation theory.
We demonstrate that, by changing the direction of the chirp in vacuum-ultraviolet pulses, one can switch between excitation and ionization with very high contrast, if the carrier frequency of the light is resonant with two bound states. This is a surprising consequence of rapid adiabatic passage if extended to include transitions to the continuum. The chirp phase locks the linear combination of the two resonantly coupled bound states whose ionization amplitudes interfere constructively or destructively depending on the chirp direction under suitable conditions. We derive the phenomenon in a minimal model and verify the effect with calculations for helium as a realistic example.
A computer simulation code to treat atomic excitation and laser beam propagation simultaneously in an atomic laser isotope separation system has been developed. The three- level Bloch-Maxwell equations are solved numerically to analyze the change of pulse shapes, the modification of laser frequencies and the time-varying atomic populations. The near- resonant effects on the propagation of frequency chirped and non-chirped laser pulses have been analyzed. It was found that there are serious differences in pulse shapes, frequency modifications and propagation velocities between laser pulses with and without chirping.