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Europhysics Letters (EPL)

Quantum fluctuations in strong field ionization

Dejia Dai, Libin Fu

Published Jul 1, 2021• 1 citation
Publisher

Abstract

Based on the field quantization, the angular distribution of the ionization rate of hydrogen atoms with the effect of a finite number of photons is computed in this letter. We find that the angular distribution of the ionization rate will fluctuate with the initial photon number of the field, and have a peak value higher than that predicted by Keldysh-Faisal-Reiss theory. This ionization peak is the embodiment of quantum effect. Furthermore, our calculations show that the phenomenon of ionization peak also exists when the initial field state is a coherent state.

DOI
10.1209/0295-5075/ac1649

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Based on the field quantization, the angular distribution of the ionization rate of hydrogen atoms with the effect of a finite number of photons is computed in this letter. We find that the angular distribution of the ionization rate will fluctuate with the initial photon number of the field, and have a peak value higher than that predicted by Keldysh-Faisal-Reiss theory. This ionization peak is the embodiment of quantum effect. Furthermore, our calculations show that the phenomenon of ionization peak also exists when the initial field state is a coherent state.
An approximate non-perturbative theory of multiphoton ionization of a hydrogen atom by two strong radiation fields is outlined. The special case is then considered for when one of the fields is of low intensity and high frequency and the other field is of high intensity and low frequency. A set of representative calculations has been performed for this case; that is, (a) angular distributions for given numbers of absorbed and emitted low-frequency photons and different geometries; (b) total cross-sections versus the strong-field intensity; (c) angular distributions summed over all the low-frequency photon exchanges, showing a fourfold symmetry in a geometry in which each ionization channel exhibits, instead, only a twofold symmetry; (d) the average energy gained by the ejected electrons. Calculations are performed for a strong low-frequency field of arbitrary polarization. In many respects, the present calculations are expected to complement those of single-field multiphoton ionization. It is hoped that the results of the calculations reported here may prompt systematic measurements also in this new class of processes, as the predictions are well within the state of the art of present multiphoton-ionization experiments.
Multiphoton ionization of hydrogen atoms by a strong multimode field when several final continuum states are populated is treated theoretically within a model based on the S-matrix formalism. The field is taken in dipole approximation, with zero bandwidth. Field-dressed Coulomb wave functions are used for the electron final states. Ionization rates are calculated for different numbers of photons absorbed in excess of the minimum number required to go into the continuum. In general, the calculated quantities are in good qualitative agreement with the corresponding experimental observations.
The dynamics of hydrogen atom in the presence of a strong radiation field of the titanium-sapphire laser is studied for the Keldysh parameters γ ≥ 1 and γ ≤ 1. It is demonstrated that the ionization is supplemented with the effective population of the excited states with the principal quantum numbers n = 5–10 in the entire range of variation in the Keldysh parameter. The population of the excited Rydberg states can be interpreted as a consequence of the multiphoton resonance involving the initial 1 s state and a group of excited states in the vicinity of the continuum boundary with the simultaneous repopulation of these states by Λ-type Raman transitions under the action of the laser field. The resulting coherent Rydberg packet appears to be stable with respect to ionization, so that the ionization of the atomic system in the presence of strong electromagnetic field is suppressed. Physical reasons for the stabilization are discussed. An interpretation of the effective population of the Rydberg states in the recent experiments on the ionization of atomic helium by the titanium-sapphire laser is proposed.
A previous theory of atomic transitions in ultrastrong electromagnetic fields is applied to the problem of the ionization of highly excited hydrogen atoms. The magnitude of the fields necessary for the validity of the theory is greatly reduced by using excited hydrogen in the initial state, and the requirement of only multiphoton ionization limits the application to lowfrequency (microwave) fields. The requirement can probably be satisfied with currently available equipment. A result of the calculation is that the average number of photons absorbed is twice the minimum number.
We consider ionization of an atom by the electromagnetic field in a Fock state $|N\ensuremath{\rangle}$: An eigenvector of the operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{N}}_{\mathbit{k},\ensuremath{\lambda}}={\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{\mathbit{k},\ensuremath{\lambda}}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{\mathbit{k},\ensuremath{\lambda}}$ of the number of photons in the mode $\mathbit{k},\ensuremath{\lambda}$. We treat the electromagnetic field in a quantized way, which allows us to obtain the photon picture of the strong field ionization. We obtain, in particular, probability distributions for the number of absorbed photons in the process of strong field ionization for atomic systems governed by short-range and Coulomb potentials.
The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.