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Journal of Physics B Atomic Molecular and Optical Physics

Adiabatic stabilization in photodetachment by ultrashort pulses

Martin Dörr, R. M. Potvliege

Published Mar 6, 2000• 21 citations
Publisher

Abstract

The stabilization of a one-dimensional delta potential model atom under the influence of a high frequency, short laser pulse is investigated, through both an ab initio numerical integration of the time-dependent Schrödinger equation and a Floquet calculation in the single-dressed-state approximation. Provided the intensity is not too high, the variation of the photodetachment probability is explained by adiabatic stabilization and its oscillating behaviour by that of the Floquet rate of photodetachment.

DOI
10.1088/0953-4075/33/6/107

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The stabilization of a one-dimensional delta potential model atom under the influence of a high frequency, short laser pulse is investigated, through both an ab initio numerical integration of the time-dependent Schrödinger equation and a Floquet calculation in the single-dressed-state approximation. Provided the intensity is not too high, the variation of the photodetachment probability is explained by adiabatic stabilization and its oscillating behaviour by that of the Floquet rate of photodetachment.
In this chapter,we shall analyze the particular case of an atom interacting with a laser pulse whose duration is sufficiently long, so that the evolution of the atom in the laser field is adiabatic. When this condition is fulfilled, the atom can be considered to interact with a monochromatic laser field. As a consequence, the Hamiltonian of the system is periodic in time, and the Floquet theory [1] can be used to solve the time-dependent Schrödinger equation (TDSE) non-perturbatively. We begin in Section 4.1 by considering the Hermitian Floquet theory. We first derive the Floquet theorem for a monochromatic, spatially homogeneous laser field and show that the solutions of the TDSE correspond to dressed states having real quasi-energies , which can be obtained by solving an infinite system of time-independent coupled equations. We then generalize the Floquet theory to multicolor laser fields and to “non-dipole” laser fields which are not spatially homogeneous. In Section 4.2, the Floquet theory is applied to study the dynamics of a model atom having M discrete levels interacting with a monochromatic laser field. In this case, the coupling between the bound and continuum atomic states is neglected.We analyze the relationship between the Floquet theory and the rotating wave approximation, and examine the perturbative limit of the Floquet theory. We also consider the population transfer between Floquet dressed states.
The influence of ultrashort low-frequency laser pulses of different intensities and pulse lengths on the dynamics of a resonantly driven atomic system is investigated theoretically. We demonstrate the periodical dependence of the total ionization rate on the appearance time of a strong few-cycle laser pulse. By depleting the excited state, the intense short pulse not only resets the Rabi oscillations, but also introduces a time shift that is proportional to the pulse length. This time shift can be employed to determine the ultrashort pulse length. In the case of ultrashort pulses with lower intensities, we observe side-bands in the two-photon ionization spectrum, whose intensities vary periodically with the appearance time of the pulse. This can be utilized to measure the period of Rabi oscillations. We have developed an S-matrix theory of two-colour ionization which can explain some of the observations of our numerical calculations. Furthermore, we have studied the high harmonic generation spectra as well as the attosecond pulses generated from the high harmonics. We show that the Rabi oscillation can be used to alter the ionization rate within laser sub-cycles and therefore select different quantum trajectories in the high harmonics generation.
We have studied population trapping in a one-dimensional model atom interacting with a short-pulse high-intensity laser, using Floquet analysis and direct numerical integration of the time-dependent Schrödinger equation for a range of peak pulse intensities. We find that photoelectrons are efficiently produced only by pulses whose peak intensities lie in a narrow range around the resonant intensity for a given intermediate state. Excited-state populations, however, are generated with comparable efficiencies for all pulses whose peak intensities exceed the resonant intensity. This implies that, for a realistic laser pulse with an inhomogeneous spatial distribution of intensity, excited atoms are generated throughout a larger volume than are photoelectrons. Interpretations of recent experiments are reexamined in light of this result.
The Floquet theorem allows one to reformulate periodic time-dependent problems such as the interaction of a many-body system with a laser field in terms of time-independent, field-dressed states, also known as Floquet states. If this was possible for density-functional theory as well, one could reduce in such cases time-dependent density-functional theory to a time-independent Floquet density-functional theory. We analyze under which conditions the Floquet theorem is applicable in a density-functional framework. By employing numerical ab initio solutions of the interacting time-dependent Schr\"odinger equation with time-periodic external potentials we show that the exact effective potential in the corresponding Kohn-Sham equation is not unconditionally periodic. Whenever several Floquet states in the interacting system are involved in a physical process the corresponding Hartree-exchange-correlation potential is not periodic with the external frequency only. Using an analytically solvable example we demonstrate that, in general, the periodicity of the time-dependent Kohn-Sham Hamiltonian cannot be restored by choosing a different initial state. Only if the external periodic potential is sufficiently weak such that the initial state of the interacting system evolves adiabatically to a single, field-dressed state, the resulting Kohn-Sham system admits the application of the Floquet theorem.
We analyze the quantum dynamics of the one-dimensional periodically kicked Rydberg atom. The time-dependent Schr\"odinger equation is solved by employing a nonunitary representation of the period-one evolution operator in a finite basis set that accounts for the outbound probability flux. We find a direct correspondence 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.
It has been widely believed that short-pulse multiphoton ionization is dominated by a resonance process: excited states of the atom are shifted by the radiation field into multiphoton resonance with the ground state, are populated, and then rapidly ionized. A recent experiment, shows significant population remaining in excited states at the end of the laser pulse, and this result has been interpreted as indicating that ionization proceeds slowly out of these states. We investigate this issue in the framework of Floquet theory, supplemented by direct numerical solution of the time-dependent Schrodinger equation. In this framework, the standard picture is portrayed as an adiabatic transition between Floquet eigenstates, which occurs as the amplitude of the laser field is ramped through the resonance value (i.e. through an avoided crossing of Floquet quasienergies). Thus it follows that the same type of transition must occur as the field is turned off. This mechanism can yield significant populations of excited states that do not suffer appreciable ionization. We exhibit this effect by numerical studies of a model atom with two bound states and two continua.