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Оптика и спектроскопия

Excitation and ionization of a particle in a one-dimensional potential well of zero radius by an extremely short light pulse

Rostislav M. Arkhipov, Mikhail V. Arkhipov, A. V. Pakhomov, N. N. Rosanov

Published Jan 1, 2022• 2 citations
Publisher

Abstract

The Migdal sudden perturbation approximation is used to solve the problem of excitation and ionization particles in a one-dimensional potential of zero radius with an extremely short pulse. There is only one energy level in such a one-dimensional the delta-shaped potential well. It is shown that for pulse durations shorter than the characteristic period of oscillations of the wave function of the particle in the bound state, the population of the level (and the probability of ionization) is determined by the ratio of the electric area of the pulse to the characteristic "scale" of the area inversely proportional to the size of localization of the particle in a bound state. Keywords: unipolar pulses, electrical pulse area, atomic scale of electric area.

DOI
10.21883/eos.2022.03.53561.2959-21

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The Migdal sudden perturbation approximation is used to solve the problem of excitation and ionization particles in a one-dimensional potential of zero radius with an extremely short pulse. There is only one energy level in such a one-dimensional the delta-shaped potential well. It is shown that for pulse durations shorter than the characteristic period of oscillations of the wave function of the particle in the bound state, the population of the level (and the probability of ionization) is determined by the ratio of the electric area of the pulse to the characteristic "scale" of the area inversely proportional to the size of localization of the particle in a bound state. Keywords: unipolar pulses, electrical pulse area, atomic scale of electric area.
The Migdal sudden perturbation approximation is used to solve the problem of excitation and ionization particles in a one-dimensional potential of zero radius with an extremely short pulse. There is has only one energy level in such a one-dimensional the delta-shaped potential well. It is shown that for pulse durations shorter than the characteristic period of oscillations of the wave function of the particle in the bound state, the population of the level (and the probability of ionization) is determined by the ratio of the electric the area of ​​the pulse to the characteristic “scale” of the area inversely proportional to the area of ​​localization of the particle in a bound state.
Using the solution of the time Schrödinger equation, the features of the excitation of a bound state of a particle in a one-dimensional rectangular quantum well of small depth by an extremely short light pulse are studied. The case of a shallow well with only one energy level is considered. In this case, the system is excited by an attosecond pulse whose duration is shorter than the characteristic time associated with the energy of the bound state of the particle in the well. It is shown that in this case the population of the bound state and the ionization probability are determined by the ratio of the electric area of the pulse to its atomic measure, which is inversely proportional to the well width. The calculation results showed that unipolar subcycle pulses with nonzero electric area can excite the system faster and more efficiently than bipolar pulses with zero area. The possibility of using unipolar gamma-ray pulses of zeptosecond duration for deuteron excitation is discussed, and numerical estimates of the required duration and electric area of the pulse are given.
We study the time evolution of the wave function of a particle bound by an attractive δ-function potential when it is subjected to time-dependent variations of the binding strength (parametric excitation). The simplicity of this model permits certain nonperturbative calculations to be carried out analytically both in one and three dimensions. Thus the survival probability of bound state |θ(t)|2, following a pulse of strength r and duration t, behaves as |θ(t)|2−|θ(∞)|2∼t−α, with both θ(∞) and α depending on r. On the other hand, a sequence of short pulses produces an exponential decay over an intermediate time scale.
Based on an approximate solution of the Schrödinger equation, the effect that a pair of extremely short small-amplitude subcycle pulses has on a quantum system is studied. It is shown that, if the pulses are shorter than the inverse frequencies of atomic transitions, the probability of transitions between levels is determined by the electric area of the pulses and the time delay between them. As a consequence, a unipolar pulse can more efficiently affect the system than a bipolar one, while a sequence of pulses realizes a selective action on quantum objects, despite a nonresonant character of the interaction.
The propagation of a unipolar light pulse with a duration of less than one period in a two-level resonant amplifying medium is studied theoretically. In the process of amplification, the unipolar pulse becomes bipolar. The effect of the relaxation time on the shape and duration of the amplified pulse is demonstrated. It is found that the electric pulse area (integral of electric field strength with respect to time) is conserved, in contrast to the area under the long pulse envelope (integral of slowly varying field amplitude with respect to time), which, in the case of long pulses, satisfies the McCall – Hahn area theorem.